1. Suppose you selected a random sample of n = 29 measurements from a normal distribution. Compare the standard normal z value with the corresponding t value for a 95% confidence interval. 2. A coin is flipped 6 times. The variable x represents the number of tails obtained. List the possible values of x. Is x discrete or continuous? Explain. 3. Suppose (1,000, 2,100) is a 95% confidence interval for ?ª . To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Explain why an increase in sample size will lead to a narrower interval of the estimate of ?ª . 4. IA hospital reports that two patients have been admitted who have contracted Crohns disease. Suppose our experiment consists of observing whether each patient survives or dies as a result of the disease. The simple events and probabilities of their occurrences are shown in the table (where S in the first position means that patient 1 survives, D in the first position means that patient 1 dies, etc.). Simple Events Probabilities SS 0.58 SD 0.16 DS 0.15 DD 0.11 Find the probability that neither patient survives.5. A random sample of n = 15 observations is selected from a normal population to test H0: ?ª = 2.89 against Ha: ?ª < 2.89 at ?¤ = .01. Specify the rejection region. 6. The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 5400 miles. If the manufacturer guarantees the tread life of the tires for the first 53,520 miles, what proportion of the tires will need to be replaced under warranty? 7. An automobile manufacturer has determined that 30% of all gas tanks that were installed on its 2002 compact model are defective. If 14 of these cars are independently sampled, what is the probability that more than half need new gas tanks?8. The ages of five randomly chosen professors are 62, 59, 51, 60, and 41. Calculate the sample variance of these ages. 9. If the odds against winning a game are 3 to 4, what is the probability of winning the game?