People in a random sample of 236 students enrolled at a liberal arts college were asked questions about how many hours of sleep they get each night (“Alcohol Consumption, Sleep, and Academic Performance Among College Students,” Journal of Studies on Alcohol and Drugs [2009]: 355–363). The sample mean sleep duration (average hours of daily sleep) was 7.71 hours and the sample standard deviation was 1.03 hours. The recommended number of hours of sleep for college-age students is 8.4 hours. Is there convincing evidence that the population mean sleep duration for students at this college is less than the recommended number of 8.4 hours? Test the relevant hypotheses using α = 0.01.