Sleep deprivation study. In a British study, 12 healthy college students deprived of one n...

Sleep deprivation study. In a British study, 12 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 12 sleep-deprived students had a mean of  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 α =.05.

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b. What assumption is required for the hypothesis test of part a to be valid?