The mean score on the SAT Math Reasoning exam is 516. A test preparation company states that the mean score of students who take its course is higher than 516.
(a) Determine the null and alternative hypotheses.
(b) If sample data indicate that the null hypothesis should not be rejected, state the conclusion of the company.
(c) Suppose, in fact, that the mean score of students taking the preparatory course is 522. Has a Type I or Type II error been made? If we tested this hypothesis at the α = 0.01 level, what is the probability of committing a Type I error?
(d) If we wanted to decrease the probability of making a Type II error, would we need to increase or decrease the level of significance?