Problem:

A company that sells an online course aimed at helping high-school students improve their SAT scores has claimed that SAT scores will improve by more than 90 points on average if students successfully complete the course. To test this, a national school counseling organization plans to select a random sample of n = 100 students who have previously taken the SAT test. These students will take the company's course and then retake the SAT test. Assuming that the population standard deviation for improvement in test scores is thought to be 30 points and the level of significance for the hypothesis test is 0.05,

Required:

Find the critical value in terms of improvement in SAT points, which would be needed prior to finding a beta.

A) Reject the null if SAT improvement is > 95 points.
B) Reject the null if SAT improvement is > 94.935 points.
C) Reject the null if SAT improvement is > 95.88 points.
D) Reject the null if SAT improvement is 85.065 points.

Solve the problem and show all work.