13.8 Assume that, on average, healthy young adults dream 90 minutes each night, as inferred from a number of measures, including rapid eye movement (REM) sleep. An investigator wishes to determine whether drinking coffee just before going to sleep affects the amount of dream time. After drinking a standard amount of coffee, dream time is monitored for each of 28 healthy young adults in a random sample. Results show a sample mean, X, of 88 minutes and a sample standard deviation, s, of 9 minutes.

a) Use t to test the null hypothesis at the .05 level of significance.

b) If appropriate (because the null hypothesis has been rejected), construct a 95 percent confidence interval and interpret this interval.

13.10 Even though the population standard deviation is unknown, an investigator uses z rather than the more appropriate t to test a hypothesis at the .05 level of significance.

1. Is the true level of significance larger or smaller than .05?
2. Is the true critical value larger or smaller than that for the critical z?