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# Testing A Claim About A Proportion

A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test. Independent group means, population standard deviations and/or variances unknown B. Lecture #8 Chapter 8: Hypothesis Testing This chapter introduces another major topic of inferential statistics: testing claims (or hypothesis) made about population parameters. To test this claim 12 people were put on the program and the number of pounds of weight gain/loss was recorded for each person after two years, as shown in columns A and B of Figure 1. Chi-Squared Independence Test Step 1: State the hypotheses and identify the claim. 051470 C) 37 D) 38. (We found that 326 of 460 voted. 4) Use the given sample data to test the claim that p1 > p2. Wilson in 1927 (references below). ) 222ulation Proportion XI # of Successes t Sample size Sample Proportion ( ) Steps to run a Two Sample Proportion Test: 1. Observed proportion (%): the observed proportion, expressed as a percentage. 25 (or 25%). Testing Claims about Proportions. 11) In a sample of 167 children selected randomly from one town, it is found that 37 of them suffer from asthma. Now the claim has no semblance of equality in it. Conditions/Requirements for conducting a hypothesis test about a population proportion : 1. The formula for the z test for a proportion is where 1 Friday, January 25, 13 1. Which of the following is NOT a requirement of testing a claim about a population proportion using a formal method of hypothesis testing? The lowercase symbol, p, represents the probability of getting a test statistic at least as extreme as the one representing sample data and is needed to test the claim. While it is not possible to assess this causal claim, it is still possible to test for an association using these data. According to Warren’s own DNA test, she has, at best, 1/64th Native American ancestry, but it could also be as low as 1/1,024. 50 is obtained when testing the claim t Algebra -> Probability-and-statistics -> SOLUTION: Assume the significance level is a=0. In hypothesis testing, Claim 1 is called the null hypothesis (denoted “Ho“), and Claim 2 plays the role of the alternative hypothesis (denoted “Ha“). reasonable proportion - German translation – Linguee Look up in Linguee. Hypothesis testing with the chi-square test is addressed in the third module in this series: BS704_HypothesisTesting-ChiSquare. Tests of Significance. In a random sample of 250 patients, 23 experienced nausea. We accept true hypotheses and reject false hypotheses. ! We use a hypothesis test to indicate what we believe the proportion is not. Single proportion EXERCISE 1 A new chocolate bar is taste-tested on. Use alpha. EBook Problems Set - Testing a Claim about a Proportion Problem 1. Testing a Proportion p 2 Testing a Proportion p For tests of proportions, we need to convert the sample test statistic to a z value. The Test for one proportion in the Tests menu can be used to test the hypothesis that an observed proportion is equal to a pre-specified proportion. The test will work ne either way. Can we conclude that the program is effective? Figure 1 – One sample t test. 5 and you use the BINOMIAL option on FREQ to do it. 4 Difference Between Proportions Symbols: (two of everything!) (hJP. Patients who hire this medical consultant may have lower complication rates for other reasons. A researcher claims that the proportion of college students who plan to participate in community service after graduation is greater than 35%. In this section, we looked at the four steps of a hypothesis test as they relate to a claim about a population proportion. They test the claim that 10% of Americans are left-handed. More about the z-test for two proportions so you can better understand the results yielded by this solver: A z-test for two proportions is a hypothesis test that attempts to make a claim about the population proportions p 1 and p 2. The Wisconsin Bottling Company employs 2 shifts of workers to fill bottles with ice. Now the claim has no semblance of equality in it. Chapter 11: Testing Hypotheses About Proportions Recall: last time we presented the following examples: 1. CONSTRUCT a confidence interval to draw a conclusion about for a two-sided test about a population proportion. The results are mutually exclusive. So here we find in our problem statement, it says the claim is that “polygraph results are correct less than 80% of the time. Directions: Give your answers to the short-answer items. to test the claim that the proportion is greater than 0. 001), or if the patient was between 40 and 60 years of age (24. Test this claim at the 0. 24) An entomologist writes an article in a scientific journal which claims that fewer than 12 in ten thousand male fireflies are unable to produce light due to a genetic mutation. To test this claim, we have him attempt 50 free-throws. A laptop manufacturer claims that the mean life of the battery for a certain model of laptop is less than 9 hours. Hypotheses for a two-sided test for a population mean take the following form: H0: = k Ha: k. As we learned earlier, the P-value for a hypothesis test for a population proportion comes from a normal model for the sampling distribution of sample proportions. Of note, only a proportion of studies tested for loss in all four of the MMR proteins (23/42, 55%). Conditions/Requirements for conducting a hypothesis test about a population proportion : 1. 65 has a test statistic of z = -1. We call these claims hypotheses Our starting point, the status quo, is called the null. One Proportion Z Test is a hypothesis test to make comparison between a group to specified population proportion. On Macs, if you specify the count rather than the sample proportion, press the Return key before using the Calculate button. If the test statistic is not in our critical region, then we fail to reject the null hypothesis. A) There is not sufﬁcient evidence to support the claim that the true proportion is less than 2 in ten thousand. 05 significance level to test the claim that less than 25% of adults have smoked within the past week. Hypothesis testing (or test of significance) is a procedure, based on a sample evidence and probability, used to test claims regarding a characteristic of one or more populations. You want to test to see if the proportion is actually less. If you want to test something else, then perhaps you can set it up as a contingency table for Item 1 so we can better understand the question. On this page, we look at how to determine P-values. a) A left-tailed test with = 0. 01 significance level to test the claim that the proportion of subjects who respond in favor is equal to 0. 8-2 Basics of hypothesis testing In this section, 1st we introduce the language of hypothesis testing, then we discuss the formal process of testing a hypothesis. In tests of hypothesis comparing proportions between two independent groups, one test is performed and results can be interpreted to apply to a risk difference, relative risk or odds ratio. Harry lifted his head off his pillow and went to grab his glasses, but then he noticed his right arm was pinned to the bed and had fallen asleep for lack of circulation. It is as follows: The average number of accidents in previous years in a city has been 15 per year, but this year it was only 10. B) A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test. If you want to test something else, then perhaps you can set it up as a contingency table for Item 1 so we can better understand the question. Hypothesis Test! We use a confidence interval to indicate what we believe the population proportion is. Under the Gambling Act 2005 the test is whether the person organising the competition has a reasonable expectation that the skill requirement will either deter a significant proportion of potential participants from entering or prevent a significant proportion of entrants from receiving a prize. Hypothesis Tests for One or Two Proportions. Math 1110 8. The given is a right tailed test. (We found that 326 of 460 voted. test the claim that there is no difference in the proportions of the small and large nursing homes with a resident 9. The sample size is sufficiently large ( nπ0 ≥5 and n(1−π0) ≥5) such that the sampling distribution of the sample proportion πˆ is approximately normal. Is this signi cantly lower than the proportion of all Americans who are left-handed, which is. 1 Student Learning Objectives By the end of this chapter, the student should be able to: Classify hypothesis tests by type. Under the Gambling Act 2005 the test is whether the person organising the competition has a reasonable expectation that the skill requirement will either deter a significant proportion of potential participants from entering or prevent a significant proportion of entrants from receiving a prize. Testing Claims About Proportions on Calculator This is the easiest method to test a hypothesis about a proportion: just go into the stats menu on your calculator, select the one-sample proportion test, and enter numbers directly from the word problem. sample proportion) or bigger, if the alternative to an equally divided population is that a majority of Americans favor lower immigration. As we learned earlier, the P-value for a hypothesis test for a population proportion comes from a normal model for the sampling distribution of sample proportions. In many cases, a one-sample Hypothesis test of Proportion is used to determine if one population has the same proportion as the known proportion of another population, p. And yet it also seems that there are possible worlds in which this claim would be false (e. The sample proportions p′ and q′ are calculated from the data: p′ is the estimated proportion of successes, and q′ is the estimated proportion of failures. Assume the company wants to use a 0. However, the confidence interval uses an estimated standard deviation based upon the sample proportion p. The Confidence Interval of a Proportion This unit will calculate the lower and upper limits of the 95% confidence interval for a proportion, according to two methods described by Robert Newcombe, both derived from a procedure outlined by E. Hypothesis Test! We use a confidence interval to indicate what we believe the population proportion is. Tumour-stroma ratio (TSR) is a novel potential prognostic factor in cancers and based on the proportions of stroma and tumour area. While some folks claim to be able to taste the difference between red and blue M&Ms, the good people at M&Ms attempt to give the rest of us ample opportunity to just choose our favorites to eat first from the bag. This is a lower tailed test, using a Z statistic and a 5% level of significance. for testing claims about population proportions 1) The sample observations are a simple random sample. 4 Difference Between Proportions Symbols: (two of everything!) (hJP. A significance test is a formal procedure for comparing observed data with a claim (also called a hypothesis) whose truth we want to assess. To test this claim, a random sample of 100 customers is obtained from the list of rewards customers. 36) and not a percentage (36%) 3. The confidence interval is computed based on the mean and standard deviation of the sampling distribution of a proportion. Hypothesis testing for a proportion is used to determine if a sampled proportion is significantly different from a specified population proportion. adults who agree that people who play violent video. Testing a Claim About Two Population Means. 2 proportions D. The claim is a statement about a parameter, like the population proportion p or the population mean µ. That p-hat was likely different from the p-hat in gss2016 , but was that a fluke or is there a systematic inconsistency between that claim and the data in the GSS?. Example #13 p. Provide an appropriate. In a random sample of 250 patients, 23 experienced nausea. Problems with solutions in Elementary Statistics — Basics of Hypothesis Testing; Testing a Claim about a Proportion; Testing a Claim about a Mean: 1) σ known, 2) σ not known; Testing Claim about Variation. Most tables of the F-distribution assume right-tailed tests, but that requirement may not be necessary when using technology. A random sample of 175 voters was selected and found to consist of 35 percent Republicans. Technology Toolbox: Inference for a population proportion on the TI-83/84 The TI-83/84 can be used to test a claim about a population proportion and to construct confidence intervals. Hypothesis test. For one sample, researchers are often interested in whether a population characteristic such as the mean is equivalent to a certain value. State the null and alternative hypotheses. A researcher claims that the proportion of college students who plan to participate in community service after graduation is greater than 35%. 4 Difference Between Proportions Symbols: (two of everything!) (hJP. Right tail test means we have a positive critical value with =0. The null hypothesis is a hypothesis that the proportion equals a specific value, p 0. Determining the Child’s Sex During Pregnancy Advances in medicine make. The claim is that the proportion of peas with yellow pods is equal to 0. In addition the Agresti-Coull approach is used to compute better intervals. Determine if proportion of vegetarians has grown compared to the proportion from two years ago. A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test. Testing Claims About Proportions. Example #13 p. 1) A company manager wishes to test a union leader's claim that absences occur on the different week days with the same frequencies. Required input. Say we are testing for a proportion p. A hypothesis test (or test of significance) is standard procedure for testing a claim about a characteristic of a population. However, the confidence interval uses an estimated standard deviation based upon the sample proportion p. Chapter 8-3: Testing A Claim About a Proportion Utilize sample information to test what the value of a population parameter may be— want to answer questions about particular values for a population parameter based on information in a sample We will conduct tests for: Population proportions, p Population means, Example. Example 1 An insurance company states that 90% of its claims are settled within 30 days. The first step is to identify the claim. The items selected for the Practice Test are designed to reflect a broad coverage of claims and targets that closely mirror the summative blueprint. ${z}$ = Test statistics ${n}$ = Sample size ${p_o}$ = Null hypothesized value ${\hat p}$ = Observed proportion. The test procedure, called the two-proportion z-test, is appropriate when the following conditions are met:. Census Bureau). When you are testing a proportion, it will ask for the number of trials (n) and the number of successes. The test looks at the proportion (p) of individuals in the population who have a certain characteristic — for example, the proportion of people who carry cellphones. (We found that 326 of 460 voted. To test this claim, a random sample of 100 customers is obtained from the list of rewards customers. State a conclusion 1. 05 significance level to test the stated claim. Hypothesis Testing for the Difference Between Two Dependent Means Using the TI-84 (T-Test) - Duration: 18:10. A researcher selected a sample of 50 residents from each of three different cities to determine if they were willing to participate in a medical experiment. For example, if you expect the proportion of male births to be 50 percent, but the actual proportion of male births is 53 percent in a sample of 1000 births. One Proportion Z Test Calculator. A) There is not sufﬁcient evidence to support the claim that the true proportion is less than 2 in ten thousand. Elementary Statistics (12th Edition) answers to Chapter 8 - Hypothesis Testing - 8-3 Testing a Claim About a Proportion - Basic Skills and Concepts - Page 408 5 including work step by step written by community members like you. Provide an appropriate. More about the z-test for two proportions so you can better understand the results yielded by this solver: A z-test for two proportions is a hypothesis test that attempts to make a claim about the population proportions p 1 and p 2. Now, let's turn our attention for a bit to testing whether one population proportion p 1 equals a second population proportion p 2. This Concept introduces students to testing a claim about a proportion. @momathtchr. Chapter 9: Testing a Claim Section 9. The Confidence Interval of a Proportion This unit will calculate the lower and upper limits of the 95% confidence interval for a proportion, according to two methods described by Robert Newcombe, both derived from a procedure outlined by E. Step 1: Determine the hypotheses. Technology Toolbox: Inference for a population proportion on the TI-83/84 The TI-83/84 can be used to test a claim about a population proportion and to construct confidence intervals. Recognize type I and type II errors. Condition Number Proportion. State the Null Hypothesis H 0. Then we discuss the popular p-value approach as alternative. A random sample of 35 bottles from the day shift yields a mean and. CONDUCT a significance test about a population proportion. C) There is sufﬁcient evidence to support the claim that the true proportion is greater than 2 in ten thousand. A random sample of 100 customers yielded 18 who did in fact drink another brand of soft drink on a regular basis. The test procedure, called the two-proportion z-test, is appropriate when the following conditions are met:. Hypothesis testing in statistics is a way for you to test the results of a survey or experiment to see if you have meaningful results. So far, all of our examples involved testing whether a single population proportion p equals some value p 0. State a conclusion 1. CONSTRUCT a confidence interval to draw a conclusion about for a two-sided test about a population proportion. Is this signi cantly lower than the proportion of all Americans who are left-handed, which is. You’re basically testing whether your results are valid by figuring out the odds that your results have happened by chance. State: We want to perform a test at the α= 0. When testing a claim about the value of a population proportion, the requirements for approximating a binomial distribution with a normal distribution are needed. Example State DMV records indicate that of all vehicles undergoing emissions testing during the previous year, 70% passed on the first try. Smoking: In a Gallup poll of 1018 adults, it was found that 22% smoked cigarettes in the past week. Then ^p = X n is the sample proportion. Learning Objectives + 2 EXAMPLE: Suppose a basketball player claimed to be an 80% free-throw shooter. Using the TI-83/84 Plus Chapter 8: Hypothesis Testing - One Sample Here we see how to use the TI 83/84 to conduct hypothesis tests about proportions and means. Introductory Statistics Lectures Testing a claim about two proportions Two sample hypothesis test of the proportion Anthony Tanbakuchi Department of Mathematics. A) If you want to test a claim about population proportions, use the P-value method or the classical method of hypothesis testing. The Confidence Interval of a Proportion This unit will calculate the lower and upper limits of the 95% confidence interval for a proportion, according to two methods described by Robert Newcombe, both derived from a procedure outlined by E. Chapter 9: Testing a Claim Example 4: Several cities have begun to monitor paramedic response times. The problem asks for a difference in proportions, making it a test of two proportions. The alternative hypothesis stands. You sample 150 men, and 90% own cats. 1: Testing Where a Proportion Is Statistical Inference: Confidence Intervals vs. UTI test used by GPs gives wrong results in at least a fifth of cases, study claims The findings imply that a large proportion of women who seek medical help. This hypothesis test analyzes a single sample to determine if the population from which the sample was taken has a proportion that is equal to a constant, p. Which of the following situations involves testing a claim about a single population proportion? A. Under the null hypothesis that the set is empty, that is, the probability of obtaining an ele-ment is = 0, an imperfect classification process is the only way to obtain a positive count, X. 017 using the test on the calculator). Therefore, the conversion of to z follows the formula 3. On this page, we look at how to determine P-values. In Section 8-3, Example 1, we have n = 726 and x = 668 successes. The confidence interval is computed based on the mean and standard deviation of the sampling distribution of a proportion. " First select the format of the original claim that is to be tested. np 0 ≥10, where p0 is the assumed population proportion from H0. Identify the test as left tail, right tail, or two tail. The first H a is called a two-sided test since "not equal" implies that the true value could be either greater than or less than the test value, p o. “Test Results Confirm GOP Candidate Misled Employers about His Race. Recognize situations that call for testing a claim about a population proportion or estimating a population proportion. ${z}$ = Test statistics ${n}$ = Sample size ${p_o}$ = Null hypothesized value ${\hat p}$ = Observed proportion. The 1 proportion test is a basic statistical test commonly used to confirm or debunk claims. This website uses cookies to ensure you get the best experience on our site and to provide a comment feature. A random sample of 1000 Americans aged 65 and older was collected in 1980 and found that 15% had "hazardous" levels of drinking, which is defined as regularly drinking an amount of alcohol that could cause health problems given the subject's medical conditions. In fact, physicians used to ask new mothers. Find the test statistic, rounded to two decimal places. 1 Introduction to Hypothesis Testing The problem with applying the techniques learned in Chapter 5 is that typically, the popula-tion mean ( ) and standard deviation (˙) are not known. This handout will take you through one of the examples we will be considering during class. A statistical data reported that 23% voted for Republican Party in last election. whether the conditions for using a one-proportion z-test are met assuming the researcher wanted to test to see if the proportion dreaming in color had changed since the 1940's. 05, test the claim that the proportions who will participate are equal. Significance Test (or Hypothesis Testing) is a formal way to compare observed. 2 Tests About a Population Proportion After this section, you should be able to… CHECK conditions for carrying out a test about a population proportion. In Exercises, test the given claim. Center and are asked to test a claim that the proportion of. A consumer group asks the state insurance commission to investigate. We expect the sample mean to be around 3 hours. A drug manufacturer claims that fewer than 10% of patients who take its new drug for treating Alzheimer’s disease will experience nausea. Click Create Assignment to assign this modality to Significance Test for a Proportion. D) Both the traditional method and P-value method use the same standard deviation based on the claimed proportion p, but the confidence interval uses an estimated standard deviation based on the sample proportion. Which of the following is NOT a requirement of testing a claim about a population proportion using a formal method of hypothesis testing? The lowercase symbol, p, represents the probability of getting a test statistic at least as extreme as the one representing sample data and is needed to test the claim. Click here for the Spreadsheet Project 12 instructions. adults who agree that people who play violent video. UTI test used by GPs gives wrong results in at least a fifth of cases, study claims The findings imply that a large proportion of women who seek medical help. Hypothesis Testing Step 1: State the Hypotheses. a claim that is being tested, or something you hope is true. Independent group means, population standard deviations and/or variances unknown B. A) If you want to test a claim about population proportions, use the P-value method or the classical method of hypothesis testing. A researcher believes that the proportion of boys at birth changes under severe economic conditions. Chi-Squared Independence Test Step 1: State the hypotheses and identify the claim. When testing the claim that the proportion of adults who use cell phones while driving is equal to 75%, the TI83/84 Plus calculator display in the margin is obtained. For example, suppose a phone company claims that 90% of its customers are satisfied with their service. Hypothesis test In statistics, a hypothesis is a claim or statement about a property of a population. STA 2023: Statistics: Testing a Claim About a Proportion We hope that you will find this guide helpful in locating materials pertaining to statistics for your class and studies. P – The proportion of graduate students seeking housing. where p 0 is a hypothesized value of the true population proportion p. Problems with solutions in Elementary Statistics — Basics of Hypothesis Testing; Testing a Claim about a Proportion; Testing a Claim about a Mean: 1) σ known, 2) σ not known; Testing Claim about Variation. How to do a Hypothesis Test of a Claim About a Proportion using your TI-83 graphing calculator's 1-PropZTest. When you are testing a proportion, it will ask for the number of trials (n) and the number of successes. In this section, we looked at the four steps of a hypothesis test as they relate to a claim about a population proportion. 05 significance level to test the stated claim. In a group of 371 Pitt students, 42 were left-handed. Among 306 people over the age of 55, 68 dream in black and white, and among 298 people under the age of 25, 13 dream in black and white. Thus for a 2×2 table, there are (2−1)×(2−1)=1 degree of freedom; for a 4×3 table, there are (4−1)×(3−1)=6 degrees of freedom. In this case you can’t compute a test value by calculating a z-score (you need actual numbers for that), so we use a slightly different technique. 36) and not a percentage (36%) 3. When we estimate the statistics x, pˆ (sample mean and sample proportion), we get different answers due to variability. Question: You meet a woman on the street who says she has Extra Sensory Perception (ESP) and can predict the probability of dice rolls with 70% probability. Testing Claims About the Population Mean This is probably the easiest (and most understandable) method for testing a claim about a population proportion, as long as our null hypothesis contains the condition of not equal. This is a right–tailed test at α = 0. Tests of Significance. The mean score for 63 randomly selected boys is 151 with a standard deviation of 36, and the mean score for 65 randomly selected girls is 149 with a standard deviation of 34. Additional Information and Full Hypothesis Test Examples. Holick, one of the first, classic signs of vitamin D deficiency is a sweaty head. If you want to confirm a supplier's assertion that their electronic components are less than 1% defective, you could take a random sample of components and use the 1 proportion test to determine whether or not the actual proportion defective backs up. Chapter 9: Testing a Claim Section 9. Carry your calculations to three decimal places. Null hypothesis B. ) 222ulation Proportion XI # of Successes t Sample size Sample Proportion ( ) Steps to run a Two Sample Proportion Test: 1. The sample size is 500, and the number of successes is 382. 1 percent to 1. When we estimate the statistics x, pˆ (sample mean and sample proportion), we get different answers due to variability. Two statistics students, Mike and Frank, conduct a survey to test this claim. Using Your TI-83/84 Calculator for Hypothesis Testing: The 1-Proportion z Test Dr. Everything in. Click here for the Spreadsheet Project 12 instructions. , worlds in which the meter bar is damaged or exposed to extreme heat). The sample proportions p′ and q′ are calculated from the data: p′ is the estimated proportion of successes, and q′ is the estimated proportion of failures. In criminal law, the principle of proportional justice is used to describe the idea that the punishment of a certain crime should be in proportion to the severity of the crime itself. It is as follows: The average number of accidents in previous years in a city has been 15 per year, but this year it was only 10. 75 versus Ha: p ≠ 0. In this case you can’t compute a test value by calculating a z-score (you need actual numbers for that), so we use a slightly different technique. Of these 100 doctors, 82 indicate that they recommend aspirin. Given a claim about a population, determine and alternative hypotheses. Here are the observed frequencies from four categories; 5,10,10,20. Enter your null hypothesis's proportion, sample proportion, sample size, test type, and significance level. a) A left-tailed test with = 0. Performing the test. What is the random variable? Describe in words. he United States have a sexually ans tec disease TD he director of the campus health center e es at he The National Center for Health Statistics. Six Sigma – iSixSigma › Forums › General Forums › Tools & Templates › Power Curve for One Proportion (Attribute Binomial Distribution) This topic contains 0 replies, has 1 voice, and was last updated by Lucas 4 years, 4 months ago. standard procedure for testing a claim about a property of a population. You are testing the claim that the proportion of men who own cats is significant different than the proportion of women who own cats. They each construct a confidence interval based on this sample proportion. Use your three decimal places result for p^ when calculating the Z-score. This test is not performed on data in the data table, but on statistics you enter in a dialog box. One population proportion test: Which of the following situations involves testing a claim about a single population proportion? The Centers for Disease Control estimates that 22. Exact test r esults are based on calculations using the binomial. CH9: Testing the Difference Between Two Means or Two Proportions Santorico - Page 344 Section 9-1 Testing the Difference Between Two Means: Using the Z Test Suppose we are interested in determining if a certain medication relieves patients' headaches. d) When testing claims about population proportions, the traditional method and the P-value method are equivalent in the sense that they always yield the same result. 70 for a couple. The conditions for a binomial distribution are satisfied. Go to Stat > Basic Stat > 1- proportion. 8% of Americans (ages 18 to 24) get 6 or less. You need to figure out how often you would see a differ-ence of at least 1. 05 significance level to test the claim that less than 25% of adults have smoked within the past week. In Section 8-3, Example 1, we have n = 726 and x = 668 successes. ) Evidence is collected to test the claim. For example, suppose a phone company claims that 90% of its customers are satisfied with their service. CONDUCT a significance test about a population proportion. I are as follows: Proportion: Small Samples. Null hypothesis B. Go to Stat > Basic Stat > 1- proportion. So far, all of our examples involved testing whether a single population proportion p equals some value p 0. the value in. This allows us to compare two unknown proportions and infer if they are not equal to each other or if one is greater than another. The given is a right tailed test. You sample 150 men, and 90% own cats. Question 1109904: You are testing the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats. The claim is a statement about a parameter, like the population proportion p or the population mean µ. For example, if you expect the proportion of male births to be 50 percent, but the actual proportion of male births is 53 percent in a sample of 1000 births. Test this claim at the 0. So here we find in our problem statement, it says the claim is that “polygraph results are correct less than 80% of the time. Required input. 05 significance level, test the claim that the proportion of all children in the town who suffer from asthma is 11%. The z score of a given observation x, in a sample of size n, is simply (x - average of the sample) divided by the standard deviation of the sample. Hypothesis Testing: Testing a Claim using Technology (TI-83/84+) The TI-83/84+ calculators are a powerful tool for hypothesis testing. A) There is not sufﬁcient evidence to support the claim that the true proportion is less than 2 in ten thousand. • Write a claim for a hypothesis test Hypothesis test • A process that uses sample statistics to test a claim about the value of a population parameter. A claim stating that the content in one or more nutrients, other than vitamins and minerals, has been increased, and any claim likely to have the same meaning for the consumer, may only be made where the product meets the conditions for the claim ‘source of’ and the increase in content is at least 30 % compared to a similar product. np 5 and nq 5 Exercise 1. When testing a single population proportion use a normal test for a single population proportion if the data comes from a simple, random sample, fill the requirements for a binomial distribution, and the mean number of success and the mean number of failures satisfy the conditions: np > 5 and nq > n where n is the sample size, p is the. State the Null. 4 – Hypothesis Testing Two major activities of inferential statistics: 1. To test this claim, an independent researcher gathered a simple random sample of 200 customers and asked them if they are satisfied with their service, to. A drug manufacturer claims that fewer than 10% of patients who take its new drug for treating Alzheimer’s disease will experience nausea. We express the results of a significance test in terms of a probability that. In one such city, the mean response time to all accidents involving life-threatening injuries last year was μ=6. The claim is that the proportion of peas with yellow pods is equal to 0. ! The difference is in the emphasis “is” vs. test in R), or a z-score test, however, I was unable to replicate his p-values. Hypothesis Testing of Two Means and Two Proportions: Homework For questions 1-7, indicate which of the following choices best identifies the hypothesis test. Exact test r esults are based on calculations using the binomial. Want to test a claim about the proportion of a population who have a certain trait.


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# Does SWR change along the length of a transmission line?

Wikipedia says "SWR is defined as the ratio of the partial standing wave's amplitude at an antinode (maximum) to the amplitude at a node (minimum) along the line".

Standing wave voltage nodes and anti-nodes appear at points which are odd and even multiples of 1/4 wave length back from the junction of a transmission line and an antenna if there is a mismatch, and everyone knows that when there are standing waves the impedance along a transmission line changes depending on the distance from the load.

Knowing that SWR is totally dependent on the ratio of the impedance of the transmission line to load, does this mean an SWR meter must be placed at a voltage node or anti-node to get an accurate reading ? Or is the SWR constant everywhere along the transmission line ?

When i move my SWR meter along a coaxial transmission line the reading changes depending on where along the line the SWR meter is, why is this ? I checked and there is no RF current flowing on the outside of the coax so that's not the reason.

The $$SWR$$ is, in principle, defined as a ratio of maximum and minimum voltages that exist at different locations of the transmission line. These two different voltages $$U_{max}$$ and $$U_{min}$$ can be measured to determine $$SWR$$. - However, $$SWR$$ can also be determined by the absolute value of the reflection coefficient, $$|\Gamma |$$, according to $$SWR = \frac{1+|\Gamma |}{1 – |\Gamma |} = \frac{U_{max}}{U_{min}} = \frac{U_{forward}+U_{return}}{U_{forward}-U_{return}}$$ $$|\Gamma | = \sqrt{\frac{P_{return}}{P_{forward}}}=\frac{U_{return}}{U_{forward}}$$ The absolute value of the reflection coefficient, $$|\Gamma |$$, is the square-root of the ratio of return-power to forward-power, both now measured at one and the same location along the feedline (e.g., coax) to determine $$SWR$$. Equally, one can measure the forward voltage and return voltage at the same location, or their sum and their difference to determine $$SWR$$.

Yes, the $$SWR$$ can change along the transmission line. This is the case if the line is lossy. The $$SWR$$ is constant along the transmission line if the line is, or may be considered, lossless.

Assume we are at the end of the transmission line. The mismatch between load and characteristic impedance of the line determines the reflection coefficient and $$|\Gamma |$$, which is the square-root of the ratio of return-power to forward-power at the end of the feedline. Now, we move away from the end of the line und closer to the feedline input; we consider a lossy line. At the new location, the forward-power is higher than the forward-power reaching the end of the line, due to the attenuation of the line. But the return-power at the new location is lower than measured at the end of the line because it has been attenuated along its path from the end of the line to the new location. Consequently, with lower return-power and higher forward-power, the ratio, $$|\Gamma |$$, i.e., the square-root of the ratio of return-power to forward-power at the new location is smaller than measured at end of the line. The smaller the $$|\Gamma |$$, the smaller and closer the $$SWR$$ gets to 1. (The same discussion can be presented in terms of forward and return voltages, of course.)

Your observation of $$SWR$$ changing along a (lossy) line confirms that $$SWR$$ measurements are best performed at the load if one wishes to determine the actual load mismatch.

For a lossy line, in a Smith-Chart the transformed load impedance moves along a spiral, which is the curve of the complex reflection coefficient, $$\Gamma$$. Asymptotically, the spiral merges into the center of the chart, as the distance to the load becomes longer and longer. At the center of the Smith-Chart, the transformed load impedance equals the characteristic impedance of the feedline; the reflection coefficient becomes zero, i.e., $$\Gamma =0$$ and consequently $$SWR=1$$. If the lossy line gets very long, at the input we will no longer feel the actual mismatch that might exist at the far end of the line. Therefore, the $$SWR$$ measurement at the input of a long feedline can significantly underestimate the $$SWR$$ given at the load side. Perhaps, in practice one might like to keep this in mind.

The following Smith chart shows an example of a very lossy line to see the effect. Example: 50Ω lossy feedline terminated into 200Ω (DP 1), i.e., $$(V)SWR=4$$ at load. Two circles of constant $$(V)SWR$$ (4 and 2) are shown in green.

In the above equations, all values $$U_{forward}$$, $$U_{return}$$, their sum $$U_{forward}+U_{return}$$, their difference $$U_{forward}-U_{return}$$, and the power values of $$P_{forward}$$ and $$P_{return}$$ refer to the one location of the SWR-measurement. We can perform the measurement anywhere along the line (keeping in mind the measured $$SWR$$ on a lossy line decreases as we move away from load). We do also not need to relocate the meter for two separated measurements, provided we obtain by the applied meter-principle two values which allow to separate and to obtain, directly or indirectly, the forward component and the return component that both apply at the single location of our measurement at any spot selected along the line. With the knowledge of forward component and return component, we know the reflection coefficient and $$|\Gamma |$$ and, thus, we know $$SWR$$.

Now, assume the measurement principle allows us to obtain only the phase-dependent superposition of forward voltage and return voltage; this location-dependent superposition is the (transversal) voltage of the standing wave. From this single value, we are no longer able to separate the result into forward component and return component. Also, we might have no idea where our measurement location is relative to the phase of the standing wave on the line. However, in this case we can search for the positions of the maximum and minimum standing-wave voltages along the line, with the ratio of the measured voltages $$(U_{max}/U_{min}$$) being the SWR. (Any transmission line loss between the two measurement positions (separated by $$\lambda /4$$) is usually neglected.) But this measurement principle appears meanwhile as heritage from the past (photo; credit: QST-Magazine), although the principle might appear closer to the (original) definition of $$SWR$$.

• Jens, thanks for the answer, to be clear, for an ideal lossless line, the SWR is constant along the length of the line ? May 29 at 23:04
• So if i place the SWR meter half way between voltage nodes the reading will still be correct ? May 30 at 2:34
• @Andrew: Thank you for your response. Yes, for a lossless line the SWR is constant along the line (perfect circle in Smith-Chart).
– Jens
May 30 at 19:12
• @Andrew: Yes, with usual SWR-meters the measurement can be performed anywhere along the line, i.e., is still correct also half-way between voltage nodes (if one knows this location). For a more detailed reply, see addition in Answer above.
– Jens
May 30 at 19:14
• Jen, thanks you for your efforts to explain this. To summarize, when using an older SWR meter which measures the phase-dependent superposition of forward voltage and return voltage, the forward and reflected components of the standing wave cannot be separated and the measurements must be made at a standing wave node and anti-node, whereas more modern SWR meters are able to distinguish between the ratio of forward and reflected current, and this kind of measurement can be made anywhere along the line as the ratio of forward and reflected current is the same everywhere along the line. May 31 at 10:34

format: plain


text:
# Why does merge sort work for any $n$, but the basic FFT algorithm only for powers of $2$?

Merge sort and FFT are both divide and conquer algorithms that split the input in two repeatedly. While merge sort can be applied to any $$n$$, the FFT algorithm given in CLRS (section 30.2, third edition) only applies when $$n$$ is a power of $$2$$. How come we can forge ahead with any $$n$$ for merge sort, but not quite for FFT?

• I think the recursive step works fine, but the problem is the halving lemma (lemma 30.5) Nov 25 at 1:07
• Hi @Rohit, I think you're right, at least for $n$ odd. The first edition even says about the Halving lemma, "if $n>0$ is even,...". Again, for $n$ odd, when you take powers greater than $n/2$, you run into problems, since $\left( \omega_{n/2} \right)^{n/2 +1}$ presents problems if you consider the Cancellation lemma. You would be essentially trying to get an odd power from an even power, or vice versa. Nov 25 at 4:14

The FFT works on pairs of elements, with no leftovers. So there must be an even number of them, and by recurrence, a power of $$2$$.
Variants of the FFT can be based on other primes, and can be combined to work for composite $$n$$, but they don't reach the efficiency of binary FFT.


text:
# How to prevent rounded and duplicated tick labels in pgfplots with fixed precision?

I have a plot whose y axis is linear with fixed precision and without scaling.

\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}

\begin{document}
\begin{tikzpicture}
\begin{axis}[domain=-0.1:0.1,
yticklabel style={scaled ticks=false,
/pgf/number format/fixed,
/pgf/number format/precision=3}]
\end{axis}
\end{tikzpicture}
\end{document}

The y tick labels are very little expressive because pgf rounded 0.0005 to 0.001 in the middle, producing contradictive labels. I do not really want to increase the precision (space constraints on the page), so apparently the best solution is to remove the middle "(-)0.001" ticks. Is there a pgfplots option to achieve this? One that says "do not place ticks such that the label gets rounded", "minimum difference between labels should be 0.001" or similar.

There are literally 100 similar plots in my document coming from data which is subject to change, so manually specifying the y ticks is not the preferred option.

• I would prefer them not to be scaled, because 100 plots, each with different scaling, would be confusing. But yes, maybe adding some (fixed?) scaling is the best solution if what I want to do isn't possible. – Sören Schulze Jun 6 '15 at 15:17

One possibility is to compare whether the trimmed version is different than the original tick number. But this is quite a general spec so if your other 99 plots have different strange intervals I don't think this would be foolproof

\documentclass{standalone}
\pgfplotsset{compat=1.12}
\begin{document}
\begin{tikzpicture}
\begin{axis}[domain=-0.1:0.1,
yticklabel style={scaled ticks=false,
/pgf/number format/fixed,
/pgf/number format/precision=3},
yticklabel={%
\pgfmathprintnumberto[verbatim,fixed,precision=3]{\tick}\possiblytrimmedtick%
\pgfmathparse{\possiblytrimmedtick == \tick ? int(1):int(0)}%
\ifnum\pgfmathresult>0\relax$\tick$\else\fi%
}
]


text:
# Wave Physics

This topic is 4874 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Hi there. I have a small problem regarding wave physics. I've taken this algorithm :
void CWave::update()
{
float n;
float temp;
float one_over_dampf = 1.0f / DampingFactor;

int h;
register int v;

//Skip the edges to allow area sampling
for(h = 1; h < mHorizontalSize; ++h)
{
for(v = 1; v < mVerticalSize; ++v)
{
n = (	mWave2[v - 1][h    ] +
mWave2[v + 1][h    ] +
mWave2[v    ][h - 1] +
mWave2[v    ][h + 1]) * 0.5f - mWave[v][h];

n -= n * one_over_dampf;

mWave[v][h] = n;
}
}

//wave=wave2

for(h = 0; h <= mHorizontalSize; ++h)
{
for(v = 0; v <= mVerticalSize; ++v)
{
temp = mWave2[v][h];
mWave2[v][h] = mWave[v][h];
mWave[v][h] = temp;
}
}
}

which is basically an update algo for a water wave. Now I've been told that water waves and explosion waves are relatively the same. The thing is, does anyone know how to prevent the waves from bouncing off the edges? I found this algo from a site that I can't remember and that guy who used it got it from the Programming Gems book. So, anyone have any ideas? Thanks a lot!

##### Share on other sites
To stop it bouncing set the values at the edges equal to the values one index in from the edges after each update (and only bother updating the internal points). Look up "boundary conditions".

Incidently - you can avoid that slow memory copy by using pointers (not 2D arrays) and just swapping pointers between updates.

##### Share on other sites
Thanks a lot!

So you will only update, lets say if h is the horizontal width and v the vertical height, x=1 to h-1 and y=1 to v-1 (if x and y are variables of a for statement) ?

And what about the corners?

Sorry about all the questions, I'm really desperate. =|

Thanks again.

##### Share on other sites
Yes, that's right. Corners don't matter since they never actually get referenced - you can set them to anything you like.

##### Share on other sites
Hi again.
I've done the changes and the waves don't bounce but I get a weird disturbance in the middle of the process.

Here's what I did:
void CWave::update(){    float n;    //float temp;    float one_over_dampf = 1.0f / DampingFactor;        int h;    register int v;        //Skip the edges to allow area sampling    for(h = 1; h < mHorizontalSize; ++h)	{        for(v = 1; v < mVerticalSize; ++v)		{            n = (	mWave2[v - 1][h    ] + 					mWave2[v + 1][h    ] + 					mWave2[v    ][h - 1] + 					mWave2[v    ][h + 1]) * 0.5f - mWave[v][h];            			n -= n * one_over_dampf;                        mWave[v][h] = n;						if(h == 1)			{				mWave2[v][0] = n;			}			else if(h == mHorizontalSize - 1)			{				mWave2[v][mHorizontalSize] = n;			}						if(v == 1)			{				mWave2[0][h] = n;			}			else if(v == mVerticalSize - 1)			{				mWave2[mVerticalSize][h] = n;			}        }    }        //swap wave1 and wave2        float **temp = mWave;    mWave = mWave2;    mWave2 = temp;}

Sorry to be a bother like this.

But thanks!

##### Share on other sites
Your loop goes up to mHorizontalSize and mVerticalSize yet you reference v+1 and h+1 - out of the array bounds. This might be causing your disturbance.

The other reason for your disturbance is that the simulation may be unstable. The (1 dimensional) wave equation is:

d2h/dt2 = c^2 d2h/dx2

(d2h/dt2 is the second derivative of h with respect to time, c is the wave speed).

Then this equation is discretised - second derivative terms can be written like this:

d2h(i)/dx2 = (h(i-1) + h(i+1) - 2*h(i))/dx^2

The d2h/dt2 term is done in the same way - a nieve implementation would need you to store 3 arrays of h (one for time t+dt, one for time t, one for time t-dt), but your implementation avoids this by overwriting one of the arrays as it goes.

Anyway, the thing is that your implementation is missing various terms like c, dt and dx - in effect you've set dx and dt to be 1 (with maybe a constant term I can't be bothered to work out). This is a bad thing to do, because the implementation is only stable if:

c^t dt^2 / dx^2 < 0.5

(this is known as the Courant-Friedrichs-Lewy or CFL criterion for stability), and since you've dropped those terms from your code, it's not immediately clear that this criterion is being met.

I think that you need read up a little bit on how that bit of code is derived from the maths - it's really not hard. I just checked and the GPG book does have it, but if you don't have that book there's stuff on the web - e.g.

http://www.osc.edu/education/su_programs/si/si1997/projects/wave.html

(I googled for wave equation discrete)

When you've rewritten that bit of code with the dx, dt and c terms, then you should choose the dt value such that the CFL criterion is satisfied - and in general is more than satisfied - for example choose dt such that

c^t dt^2 / h^2 = 0.05

since smaller dt values will also lead to a more accurate result.

I know it's tempting just to filch working physics code and plug it in... but unless you understand the basics behind it it tends to do wierd things!

Edit: Changed the link to one that remembers to include the dx/dt terms!!

[Edited by - MrRowl on September 5, 2005 4:14:03 PM]

##### Share on other sites
Thanks a lot MrRowl.

The thing is in our project I wasn't originally in charge with the physics but another guy in our group couldn't continue anymore so I had to take over and I honestly havn't got a clue why he did it like that thats why I tried playing around with it and posting here to find some answers.

And the mHorizontal size thing is correct because in the landscape my friend who is no longer with our group made the width and height of the arrays to be [mVerticalSize + 1][mHorizontalSize + 1] so if you check if something <= mVerticalSize then you're checking if something is < mVerticalSize + 1. Get it? I really want to change that because its pretty confusing sometimes and unnessasary.

Sorry I don't mean to talk bad of my friend who left, he's a good hardworking guy who didn't leave because he wanted to but because cercomstances forced him to.

Thanks again.

##### Share on other sites
Ok, I've implemented the velocities, times, etc. (got it from a tutorial) so I have:
float A = (3.0f * 0.10f / 1.0f) * (3.0f * 0.10f / 1.0f);float B = 2 - 4 * A;int   h, v;float one_over_dampf = 0.99;//Boundaries should not be updatedfor(h = 1; h < mHorizontalSize; ++h){	for(v = 1; v < mVerticalSize; ++v)	{		mWave[v][h] =	A * (	mWave2[v    ][h - 1]  + 					mWave2[v    ][h + 1]  + 					mWave2[v - 1][h    ]  + 					mWave2[v + 1][h    ]) + 				B * 	mWave2[v    ][h    ] - 					mWave [v    ][h    ];				mWave[v][h] *= one_over_dampf;				if(h == 1)		{			mWave[v][0] = mWave[v][1];		}		else if(h == mHorizontalSize - 1)		{			mWave[v][mHorizontalSize] = mWave[v][mHorizontalSize - 1];		}				if(v == 1)		{			mWave[0][h] = mWave[1][h];		}		else if(v == mVerticalSize - 1)		{			mWave[mVerticalSize][h] = mWave[mVerticalSize - 1][h];		}	}}       //swap wave1 and wave2      float **temp = mWave;   mWave = mWave2;   mWave2 = temp;

It still bounces. Sorry man, I tried a whole lot of diffrent things to stop the waves in their tracks, I've searched on the net and I even read that page you posted but no luck. I can understand if you are not going to post again. But thanks a lot so far for your help MrRowl.

##### Share on other sites
Ok, I've changed my if statement to this:

if(h == 1){	mWave2[v][0] = mWave2[v][1];}else if(h == mHorizontalSize - 1){	mWave2[v][mHorizontalSize] = mWave2[v][mHorizontalSize - 1];}if(v == 1){	mWave2[0][h] = mWave2[1][h];}else if(v == mVerticalSize - 1){	mWave2[mVerticalSize][h] = mWave2[mVerticalSize - 1][h];}

This prevented the bouncing and it still remained relatively stable but there was some bouncing back action but it was only 2 or 3 very small waves instead of 4 huge waves coming back. Any thoaghts?

##### Share on other sites
As you worked out - you need to make sure you apply the boundary condition to the correct array. It's probably simpler and "safer" to make a separate loop and apply it to mWave2 before your update since otherwise there's a danger that your boundary condition gets applied out of step at some of the edges (not got time to check if this is really the case).

Also - my suggestion for a boundary condition with mWave2[0]
• = mWave2[1]
• probably isn't good - sorry :). Some things to try:

---
mWave2[0][j] = 0; // i.e. simple fixed boundary
---
mWave2[0][j] = mWave2[1][j] + (mWave2[2][j] - mWave2[1][j]); // i.e. height gradient is continuous
---
// Gradually damp over a border zone - something like this
for (unsigned i = 0 ; i < 5 ; ++i)
mWave2[j] *= ((float) i) / 5;

and similarly for the other edges.

Sorry I don't have time to check if these are actually good ideas :) From a quick web search it seems like it's not completely trivial to totally eliminate reflected waves.

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## [f]izzbuzzer

### Looking for good programming challenges?

Use the search below to find our solutions for selected questions!

# Count ways to reach the n stair

Sharing is caring!

Problem statement
There are $n$ stairs, a person standing at the bottom wants to reach the top. The person can climb either $1$ stair or $2$ stairs at a time. Count the number of ways, the person can reach the top.

Solution
We can solve this problem recursively. If the person were to take $1$ step, then we need to solve the problem for $n-1$ stairs. That is, finding the number of ways to traverse the remaining $n-1$ stairs. If the person were to take $2$ steps then the problem gets reduced to finding the number of ways to traverse the remaining $n-2$ stairs. Assuming we have a function `count(n)` that returns the number of ways to traverse $n$ stairs, we would have:

```answer = count(n-1) + count(n-2)
```

Finally, we need to define our termination conditions:
If there only $3$ stairs left, we know that a person can traverse them in three different ways ($1+1+1$ or $1+2$ or $2+1$). If there only $2$ stairs left, we know that a person can traverse them in two different ways ($1+1$ or $2$). If there is only $1$ stair left, we know that a person can traverse them in one way only. These are our recursion-termination conditions.

• `count(3) = 3`
• `count(2) = 2`
• `count(1) = 1`

Above we can see that `count(n)` is actually equal to `fibonacci(n+1)`:

• `count(3) = fibonacci(4) = 3`
• `count(2) = fibonacci(3) = 2`
• `count(1) = fibonacci(2) = 1`

(Remember: $f_0 = 0, f_1= 1, f_2 = 1, f_3 = 2, f_4 = 3, \dots$).

We can solve this problem using the fibonacci series. Let us go ahead and define our `fibonacci(n)` function:

```public static int fibonacci(int n) {
if (n <= 1) {
return n;
} else {
return fibonacci(n-1) + fibonacci(n-2);
}
}
```

Putting it all together we have:

```public class NumberOfWays {
public static int fibonacci(int n) {
if (n <= 1) {
return n;
} else {
return fibonacci(n-1) + fibonacci(n-2);
}
}

public static int count(int s) {
return fibonacci(s + 1);
}

public static void main (String args[]) {
int s = 4;
System.out.println("Number of ways = "+ count(s));
}
}
```


text:
Transpilers, compilers and the Node.js agent

Contrast supports applications written in languages that compile to JavaScript, such as CoffeeScript and TypeScript. The Node.js only instruments JavaScript. However, if you are using CoffeeScript or TypeScript, you can configure the transpiler to compile your application into JavaScript.

Note

Although Contrast functions with languages that compile to JavaScript, the source may not correspond directly with the resulting JavaScript. As a result, reported metadata - such as vulnerability line-of-code and filename - references the compiled result, not the original source.

Some languages, like TypeScript, require you to precompile your code before runtime. In these cases, the Node.js agent must point to the compiled entrypoint for your application.

To do this, set up the Node.js agent using the -r option:

scripts: {
"test": "...",
"start": "...",
"contrast": "node -r @contrast/agent /path/to/transpiled/entrypoint.js"
}

Alternatively, languages like CoffeeScript run via a command line utility, which acts as a runner and compiles your application to JavaScript at runtime. It's possible to have Contrast's Node.js agent act as a runner for the runtime transpiler, which acts as a runner for your application. To set up Contrast as a runner:

1. Provide the entrypoint to the transpiler instead of providing the entrypoint to your application as an argument. (You're essentially telling Contrast that your application is the transpiler.)

2. Use the --appArgs setting to tell Contrast to pass this argument along.

In this example, Contrast is running with a CoffeeScript application:

scripts: {
"test": "...",
"start": "...",
"contrast": "node-contrast /path/to/coffee/transpiler --application.args '/path/to/app/entrypoint.coffee'"
}


text:
# 4.4 Resistors in series and parallel

 Page 1 / 17
• Draw a circuit with resistors in parallel and in series.
• Calculate the voltage drop of a current across a resistor using Ohm’s law.
• Contrast the way total resistance is calculated for resistors in series and in parallel.
• Explain why total resistance of a parallel circuit is less than the smallest resistance of any of the resistors in that circuit.
• Calculate total resistance of a circuit that contains a mixture of resistors connected in series and in parallel.

Most circuits have more than one component, called a resistor    that limits the flow of charge in the circuit. A measure of this limit on charge flow is called resistance    . The simplest combinations of resistors are the series and parallel connections illustrated in [link] . The total resistance of a combination of resistors depends on both their individual values and how they are connected.

## Resistors in series

When are resistors in series    ? Resistors are in series whenever the flow of charge, called the current    , must flow through devices sequentially. For example, if current flows through a person holding a screwdriver and into the Earth, then ${R}_{1}$ in [link] (a) could be the resistance of the screwdriver’s shaft, ${R}_{2}$ the resistance of its handle, ${R}_{3}$ the person’s body resistance, and ${R}_{4}$ the resistance of her shoes.

[link] shows resistors in series connected to a voltage    source. It seems reasonable that the total resistance is the sum of the individual resistances, considering that the current has to pass through each resistor in sequence. (This fact would be an advantage to a person wishing to avoid an electrical shock, who could reduce the current by wearing high-resistance rubber-soled shoes. It could be a disadvantage if one of the resistances were a faulty high-resistance cord to an appliance that would reduce the operating current.)

To verify that resistances in series do indeed add, let us consider the loss of electrical power, called a voltage drop    , in each resistor in [link] .

According to Ohm’s law    , the voltage drop, $V$ , across a resistor when a current flows through it is calculated using the equation $V=\text{IR}$ , where $I$ equals the current in amps (A) and $R$ is the resistance in ohms $\left(\Omega \right)$ . Another way to think of this is that $V$ is the voltage necessary to make a current $I$ flow through a resistance $R$ .

So the voltage drop across ${R}_{1}$ is ${V}_{1}={\mathit{IR}}_{1}$ , that across ${R}_{2}$ is ${V}_{2}={\mathit{IR}}_{2}$ , and that across ${R}_{3}$ is ${V}_{3}={\mathit{IR}}_{3}$ . The sum of these voltages equals the voltage output of the source; that is,

$V={V}_{1}+{V}_{2}+{V}_{3}.$

This equation is based on the conservation of energy and conservation of charge. Electrical potential energy can be described by the equation $\text{PE}=\text{qV}$ , where $q$ is the electric charge and $V$ is the voltage. Thus the energy supplied by the source is $\text{qV}$ , while that dissipated by the resistors is

${\text{qV}}_{1}+{\text{qV}}_{2}+{\text{qV}}_{3}.$

## Connections: conservation laws

The derivations of the expressions for series and parallel resistance are based on the laws of conservation of energy and conservation of charge, which state that total charge and total energy are constant in any process. These two laws are directly involved in all electrical phenomena and will be invoked repeatedly to explain both specific effects and the general behavior of electricity.

anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
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# Venn diagram and sets

I am stuck with this question,

In a group of 50 theatrical performers, we have 23 singers, 20 actors and 25 dancers. There are some managers who cannot perform on stage. 11 people can sing and act. 8 people can dance and act. 8 people can sing and dance. 6 people can write poetry. All poets are dancers, but 2 of them can act too. 4 people can direct plays. All directors are actors, but 2 can sing too. 5 people can sing, act and dance. Find the number of managers. How many people can only act?

The problem is somehow similar to this one but when I added up all the performer they came out to be 63 but the total team consists of 50. Is there anything wrong with my solution? Please help me out. Thanks

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How many dancers do you currently have? Or am I reading this wrong? –  tom Nov 3 '11 at 12:53
I think the problem here is that you've assumed that the 6 poets (who can all dance) are somehow separate from the 25 dancers in your crew. I think those 6 poets have to be a part of those 25 dancers, you can't just add them in separately. –  tom Nov 3 '11 at 13:02
Thanks. I got the answer now. I was missing to add the common part of all the three sets($5$). –  Fahad Uddin Nov 3 '11 at 14:01


text:
# How do you find the sum of the first 14 terms of the arithmetic series 11+7+3+...?

Mar 7, 2016

$S = - 210$

#### Explanation:

There are several formula we need to keep in mind when working with arithmetic series

1) common difference $d = {a}_{n + 1} - {a}_{n}$

2) last term : ${a}_{n} = {a}_{1} + \left(n - 1\right) d$

3) Arithmetic sum: $S = \frac{n}{2} \left({a}_{1} + {a}_{n}\right)$
An alternative formula is $S = \frac{n}{2} \left(2 {a}_{1} + \left(n - 1\right) d\right)$

Now we can begin to work this problem

We have an arithmetic series begin at 11, 7, 3 ......

We know that ${a}_{1} = \textcolor{b l u e}{11}$

Let's find the following
$d = 7 - 11 = - 4$
$\textcolor{g r e e n}{n = 14}$
${a}_{14} = 11 + \left(14 - 1\right) \left(- 4\right)$

$\textcolor{red}{{a}_{14} = - 41}$

Let's substitute it into the sum formula

$S = \frac{\textcolor{g r e e n}{14}}{2} \left(\left(\textcolor{b l u e}{11}\right) + \left(\textcolor{red}{- 41}\right)\right)$

$S = 7 \left(- 30\right)$

$S = - 210$

==============================
If we use the alternative formula, we will still get the same answer
$d = - 4 , {a}_{1} = 11 , n = 14$

$S = \frac{14}{2} \left(2 \left(11\right) + \left(14 - 1\right) \left(- 4\right)\right)$

$S = 7 \left(22 - 52\right)$

$S = 7 \left(- 30\right)$

$S = - 210$


text:
# Solution - Arithmetic Progression

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ConceptArithmetic Progression

#### Question

Write the first three terms in each of the sequences defined by the following

(i) an = 3n + 2

(ii) an = n2  + 1

#### Solution

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#### Reference Material

Solution for concept: Arithmetic Progression. For the course 8th-10th CBSE
S


text:
To recall notation from last time, given a matrix $$A\in \textrm{PSL}(n,\mathbb{R})$$ we let $$r(A)$$ denote the spectral radius, the modulus of the largest eigenvalue. We will let $$J$$ denote a Jordan block of a matrix, and will work with the convention that both the diagonal and super-diagonal have the eigenvalue (as opposed to the above-diagonal 1’s, as is standard). For example:

$J=\lambda(I+N)=\left (\begin{array}{ccc}\lambda &\lambda &0\\0&\lambda &1\\0&0&\lambda\end{array}\right)$

We define an ordering on the Jordan blocks of a matrix by considering the associated ordered pair (under the lexiographic order) $$\textrm{power}(J)=(\vert\lambda\vert,n)$$ where $$\lambda$$ is the associated eigenvalue and $$n$$ is the size of the block.

Our goal here is to describe the behavior of projective transformations, by looking at iterations of them and qualitatively describing the dynamics. However first a few definitions are in order. Given a topological space $$X$$ and a continuous map $$f:X\to X$$ we define the forward orbit of $$x\in X$$ to be the set $$\{f^n(x)\}_{n\in \mathbb{N}}$$. The $$\omega$$-limit set, denoted $$\omega(f,x)$$ is the set of accumulation points of the forward orbit, where for a subset $$U\subset X$$ we define $$\omega(f,U)=\bigcup_{x\in U}\omega(f,x)$$.

For the following defintions we will be considering positive projective space $$\mathbb{S}^n=\mathbb{P}_+(\mathbb{R}^{n+1})$$ together with its projective transformations $$\textrm{SL}^\pm(n+1,\mathbb{R})$$. Given a such projective transformation $$A$$ we may define $$E_\mathbb{C}(A)$$ to be the vector space spanned by the eigenvectors with largest modulus eigenvalue, more precisely $$E_\mathbb{C}(A)=\textrm{Span}_\mathbb{C}\{v\in\mathbb{C}^n\;\mid\; Av=\lambda v,\;\; \vert\lambda\vert=r(A)\}$$. Using this we then define $$E(A)=\mathbb{R}^{n+1}\cap E_\mathbb{C}(A)$$ and $$\mathbb{P}(E(A))$$ as its projectivization.

As a quick example, consider the map $$A=\textrm{diag}(2,2,\frac{1}{4})\in\textrm{SL}^\pm(3,\mathbb{R})$$ and let $$\Delta\subset \mathbb{S}^2$$ be the triangle with vertices $$[e_1],[e_2]$$ and $$[e_3]$$. Here $$\mathbb{P}(E(A))$$ is the projective line $$\ell$$ containing $$[e_1]$$ and $$[e_2]$$, and the forward orbit of any point in $$\Delta$$ accumulates along this line; that is, $$\omega(A,\mathring{\Delta})=\ell$$.

There’s a very useful proposition from linear algebra which will help us understand the dynamics of projective transformations such as the example above which we will state here quickly. Given any $$A\in\mathrm{SL}^\pm(n+1,\mathbb{R})$$ there is a finite collection of (positive) projective subspaces $$H_1,\ldots H_m\subset \mathbb{S}^n$$ such that if $$W$$ is a subset of their complement with nonempty interior, $$\omega(A,W)\subset \mathbb{P}_+(E(A))$$ has nonempty interior, and the action of $$A$$ not only preserves $$\mathbb{P}_+(E(A))$$ but restricts to an orthogonal action on it.

The utility of this is best illustrated by considering another example: let $$A\in \textrm{SL}^\pm(4,\mathbb{R})$$ be the following matrix

$A=\left(\begin{array}{cccc}2\cos\theta & -2\sin\theta &0&0\\2\sin\theta &2\cos\theta &0&0\\0&0&2&0\\0&0&0&\frac{1}{8}\end{array}\right)$

The eigenvalues of $$A$$ over the complex numbers are $$\{2,2e^{\pm i\theta},\frac{1}{8}\}$$, and so $$r(A)=2$$. Also, $$E_\mathbb{C}(A)$$ is the (complex) span of the first three basis vectors, and so $$E(A)=\textrm{Span}_\mathbb{R}\{e_1,e_2,e_3\}$$. The positive projectivization of $$E(A)$$ is then a 2-sphere inside of the 3-sphere, the relevant subspaces are $$H_1=[e_4]$$, $$H_2=[-e_4]$$, and the restriction of the action of $$A$$ to $$\mathbb{S}^2$$ is simply

$2\left (\begin{array}{ccc}\cos\theta &-\sin\theta &0\\\sin\theta & \cos\theta &0\\0&0&1\end{array}\right )$

which is a rotation about the “$$z$$”-axis (the overall constant factor of $$r(A)$$ doesn’t matter under projectivization). Thus we may describe the dynamics of $$A$$ acting on $$\mathbb{S}^3$$ as follows: there is a pair of two antipodal “repelling” fixed points $$H_1,H_2$$ and relative to them an equitorial 2-sphere $$S^2$$. This sphere rotates under iterations of $$A$$, and any other point of $$\mathbb{S}^3$$ is attracted towards it.

This linear-algebra-inspired description of the dynamics on $$\mathbb{S}^n$$ can be used to help us understand projective transformations preserving a more general properly convex subset $$\Omega$$. In fact; given a projective transformation $$A\in \mathrm{SL}^\pm(\Omega)$$ we can say that the largest modulus of eigenvalue for $$A$$ actually occurs as a real eigenvalue, and out of all Jordan blocks for eigenvalues of that modulus, the largest occurs for the real one (In terms of the notation we have been developing, this says that there exists a most powerful Jordan block for $$A$$ with $$\lambda=r(A)$$). Furthermore, the fixed set for this must lie on the boundary.

To see this, let $$H$$ be the union of the projective subspaces furnished for us by the linear algebra proposition above, and consider the $$\omega(A,\Omega\setminus H)$$, which is then a subset of $$\mathbb{P}_+(E(A))$$ by the proposition. Intersecting this with $$\bar{\Omega}$$ gives a compact, convex set preserved by $$A$$, and so by the Brower fixed point theorem, there is a fixed point $$x\in \mathbb{P}_+(E(A))\cap \bar{\Omega}$$. Interpreting this, we have $$[Ax]=[x]$$, and so $$Ax=\lambda x$$ for some $$\lambda>0$$. But we already know that $$x\in E(A)$$ which means that $$\vert\lambda\vert=r(A)$$, and so the radius is in fact achieved by a real eigenvalue. Also, because we began with a non-elliptic transformation, $$A$$ fixes no points in the interior of $$\Omega$$ and so our fixed point $$x$$ must lie on the boundary.

Previous Post: Lecture 8: Projective Isometries


text:
# Turning font-changing macros into font-changing “switches”

I want to turn a font-changing macro into a "switch" (I found the term in this answer), making macros like \macro{Text to be changed} work within the brakets, like {\switch text to be changed}, similarly to \textbf's and \bfseries's behavior.

I'm working with a thesis class which provides formatting commands like \titleformat, \authornameformat, etc., which can be changed. But in the whole class, those formatting commands are used like switches, so you have a \titlepage command that prints {\titleformat \titledata}, etc. I want to change some of these formatting commands into real small caps, which I defined as \DeclareRobustCommand{\smallcaps}[1]{\textls[10]{\scshape\MakeLowercase{#1}}}, but I don't know how I could make a switch to lowercase letters (i tried it with textcase package's \MakeTextLowercase too).

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[osf]{libertine}
\usepackage{letterspace}

\DeclareRobustCommand{\smallcaps}[1]{\textls[10]{\scshape\MakeLowercase{#1}}}

\begin{document}

\smallcaps{These are real smallcaps}, {\smallcaps these are not} and this is normal.

\end{document}

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In general the switch exists before the command with argument. E.g. \textbf is defined with the help of \bfseries: In latex.ltx you will find \DeclareTextFontCommand{\textbf}{\bfseries}. So you will have to be more specific about how your macro is defined if you want to go the other way round. –  Ulrike Fischer Feb 10 '12 at 17:06
Please, make a real example of usage. There's no gain in preferring the syntax {\smallcaps xyz} to \smallcaps{xyz}, in general. –  egreg Feb 10 '12 at 18:30

Let's define \textsfsl to choose \sffamily and \slshape:

\DeclareTextFontCommand{\textsfsl}{\sffamily\slshape}

The command's name need not begin with text. LaTeX will take care automatically of the italic correction for \textsfsl{text}, as can be seen in the following example:

\documentclass{article}
\DeclareTextFontCommand{\textsfsl}{\sffamily\slshape}
\begin{document}
abc \textsfsl{def}ghi

abc \sffamily\slshape def\/\normalfont ghi

abc \sffamily\slshape def\normalfont ghi
\end{document}

However, if what you need is the converse for processing section titles, there is another way: the package titlesec provides the \titleformat command, whose last mandatory argument can end with a command that takes as argument the section title: so, for example,

\documentclass{article}
\usepackage[osf]{mathpazo}
\usepackage{titlesec,microtype}
\DeclareRobustCommand{\smallcaps}[1]{\textls[100]{\scshape\MakeLowercase{#1}}}
\titleformat{\section}
{}
{\textsc{\MakeLowercase{\thesection}}}
{1em}
{\smallcaps}

\begin{document}
\section{This is my section title}
\end{document}

gives the following result

The \MakeLowercase around \thesection is to cope with possible appendices.

-
So this also holds for using it as {\textsfsl text}, I guess? –  Werner Feb 10 '12 at 17:12
Of course not: \textsfsl will take an argument, so in your example only the first "t" would be affected by the font change. –  egreg Feb 10 '12 at 17:14
Fantastic! As always. :) –  Paulo Cereda Feb 10 '12 at 17:14
@egreg: Thanks. My question was more in line with what it seems the OP is after - switches rather than macros with arguments. –  Werner Feb 10 '12 at 17:16
@Werner Let's hope that the OP makes a clearer question, then. –  egreg Feb 10 '12 at 17:32

I think you are rather looking for old font command behaviour like \bf, \tt etc. These "old" style commands can be defined using:

 \DeclareOldFontCommand{\mytt}{\sffamily\slshape}{\mathtt}

And here is a minimal as how to use them, the first parameter is the command name, followed by the normal text font declarations in the second argument. The last parameter is the math alphabet to be triggered in math mode.

\documentclass{article}
\DeclareOldFontCommand{\mytt}{\sffamily\slshape}{\mathtt}
\begin{document}
{\mytt this is a test} and this is normal.
\end{document}

The command is defined in the LaTeX kernel ltfntcmd.dtx. Definitions can also be found in all of LaTeX classes such as book and article. These type of commands have many limitations. Rather define your own semantic macros. Ideally a (La)TeX document should not have any typesetting commands in them. For example, let us say that you want to define all Ship names to be typeset as per normal English style guides that recommend they be typeset in italic. Define a macro such as:

\newcommand{\ship}[1]{\textit{#1}\xspace}

The advantage of this approach is that you can modify the macro to add them to an index as well automatically.

-
@Yannins Lazarides, the problem is that both the definition of the macro only works with switches, in the same way as \DeclareTextFontCommand. I'll rewrite the question more specifically, as required by egreg. –  henrique Feb 10 '12 at 18:13
@henrique Maybe we misunderstood you, but if you define a \myrm as well you would be able to do what you want alternative within macros \def\mymacro{{\mytt #1}} will work as well and contain its effects only within the macro. Is this what you want? –  Yiannis Lazarides Feb 10 '12 at 18:18

This one works as switch:

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[osf]{libertine}
\usepackage[letterspace=10]{letterspace}

\newcommand{\smallcaps}{\lsstyle\scshape}

\begin{document}

This is normal with some Uppercase Letters.

\smallcaps these are real smallcaps.

\normalfont This is normal with some Uppercase Letters.

{\smallcaps and these are smallcaps, again.}

\end{document}

Note, that you have to give up the use of \MakeLowercase and have therefore to mind, that you write afterwards all in small case letters. \textls is replaced by \lsstyle; the letterspace factor must be given as a package option. You should use the switch only inside of groups, because the letterspacing is otherwise not resetted, compare the first with the third sentence an my example.

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