It is generally recommended that adults sleep at least 8 hours each night. One of the authors recently asked some of her students (undergraduate and graduate students at Harvard) how many hours each had slept the previous night, curious as to whether her students are getting enough sleep. The data are displayed in Figure 1. The 12 students sampled averaged 6.2 hours of sleep with a standard deviation of 1.70 hours. Assuming this sample is representative of all her students, and assuming students need at least 8 hours of sleep a night, does this provide evidence that, on average, her students are not getting enough sleep?
(a) State null and alternative hypotheses
(b) Give the test statistic and the p-value and state the conclusion of the test.