Sleep deprivation study. In a certain study, 22 healthy college students deprived of one night’s sleep received an array of tests intended to measure their thinking time, fluency, flexibility, and originality of thought. The overall test scores of the sleep-deprived students were compared with the average score expected from students who received their accustomed sleep. Suppose the overall scores of the 22 sleep-deprived students had a mean of x = 73 and a standard deviation of 17. (Lower scores are associated with a decreased ability to think creatively.)

a. Test the hypothesis that the true mean score of sleepdeprived subjects is less than 80, the mean score of subjects who received sleep prior to taking the test. Use a = .05.

b. Write the 95% confidence interval for the testing problem.