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, what is the probability that the counseling organization will incorrectly "accept" the null hypothesis when, in fact, the true mean increase is actually 95 points?
A) Approximately 0.508
B) About 0.492
C) Approximately 0.008
D) Can't be determined without knowing the sample results.

Question

Quizplus · Accepted Answer

The probability of incorrectly accepting the null hypothesis (Type II error) can be calculated using the power of the test. Given the true mean increase is 95 points, the null hypothesis is that the mean increase is 90 points. The standard error is 30/sqrt(100) = 3. The z-score for a 95-point increase is (95-90)/3 = 1.67. The power of the test is the probability of correctly rejecting the null hypothesis, which is 1 - P(Type II error). Using the standard normal distribution, P(Type II error) is about 0.492.

A Company That Sells an Online Course Aimed at Helping