You pulled several all-nighters last semester to study for your final exams. You want to know if staying up all night hurt your exam performance so you will know if it is worth it to stay up all night...

You pulled several all-nighters last semester to study for your final exams. You want to know if staying up all night hurt your exam performance so you will know if it is worth it to stay up all night to study. You calculate the mean score for all of the finals you have ever taken in college (your exam population μ) and find that μ = 87% with σ = 5%. Assume you know that this population of scores has a normal distribution. You use as your sample the mean score on all five of the final exams you took last semester, X = 83%.

a. What are the null and alternative hypotheses for this example? Is this a one- or two-tailed test?

b. Use a one-sample z test to determine if your all-nighters hurt your performance.

c. Suppose that in reality, all-nighters do hurt your performance on exams. In this case, what type of decision has occurred in your test: correct decision, Type I error, or Type II error?