Question

Prof. Gersch knows that the amount of learning at YU is normally distributed with unknown mean and standard deviation of 2 hours. He surveys a random sample of 16 students and find that the average amount of learning that these students do per week is 19 hours. a) Construct a 95% CI for the true (pop) mean amount of learning. b) How many students should Prof. Gersch have surveyed so that the maximum margin of error in his 95% CI was 2 hours? c) Had someone told Prof. Gersch, prior to his sampling, that the true mean amount of learning was 18 hours per week, yet he thought the mean amount was greater, state the appropriate hypotheses and conduct the appropriate test at alpha of 0.05 using the sample evidence obtained. Use all possible methods here! Do the test also at alpha pf 0.01. What method is easier, why? d) Had Prof. Gersch suspected instead that the true mean amount of time spent on studying was different than 18 hours, state the appropriate hypotheses and conduct the appropriate test at alpha of 0.05 using the sample evidence obtained. Use all the possible methods here!

Answer 1

(a)

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(b)

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(c)

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(d)