According to a sociological report from 2015 US adults got an average of 7.2 hours of sleep per night. You want to know if this average has decreased since 2015. To do this you randomly select 51 US adults from across the country and determine the number of hours they sleep each night. You get an average time of 6.9 hours with a standard deviation of 1.8 hours. (a) Carry out a hypothesis test at a = .05 to test your claim that the average hours of sleep per night for US adults has decreased since 2015. Make sure to confirm all necessary conditions. State your conclusion in context of the situation. (b) Describe what it would mean to make a Type I error in this situation. (c) Describe what it would mean to make a Type II error in this situation.

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