A sample of 201 students enrolled at a liberal arts college was asked questions about how many hours of sleep they get each night. The sample mean sleep duration (average hours of daily sleep) was 7.72 hours and the sample standard deviation was 1+ a/14 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. (Use technology to calculate the P-value. Round your test statistic to two decimal places and your P-value to four decimal places.)

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