There are two basic forms of sleep: slow wave sleep (SWS) and rapid eye movement (REM) sleep.
Infants spend about 50% of their sleep time in SWS and 50% in REM sleep.
Adults below age 60 spend about 20% of their sleep time in REM and 80% in SWS sleep.
In a study of sleep patterns, data was collected on 13
elderly males over age 60. The percentage of total sleep time
spent in REM sleep is presented below.
21, 20, 22, 7, 9, 14, 23, 9, 10, 25, 15, 17, 11
- Calculate the sample average and standard deviation.
- The sample average is how far below 20%?
- Calculate the standard error (SE) of the sample average.
- The sample average is how many SE's below 20% ?
- Is the sample average significantly below 20%, or is it just chance variation?
- If you conduct a test of significance on the following hypothesis:
`Does the data provide scientific evidence that elderly males spend less than 20%
of their sleep time in REM?', how would you write the null and alternative
- What is the test statistic you would use?
- What distribution curve would you use to compute the P-value?
- Calculate a (one-tailed) P-value for your test.
- What is the conclusion of your test?