Calculating the hypothesis test for single mean.

Score-S-Up is a company that helps students improves their test scores on college entrance exams. They advertise that the study program increases a person's score on the ACT by an average of 4 points. A consumer group wishes to test if the average score increase is less than claimed 4 points. Assume the population distribution of increase in ACT scores is approximately normal with a standard deviation of 3. In September, approximately 6000 students took the ACT. Of these, 752 had taken the review course and took the ACT test for a second time. A random sample of 55 students who took the course and the ACT again is taken. The average increase of the ACT scores in sample was 3.7.

a) Perform a hypothesis test with significance level 5 percent. Demonstrate all work, and clearly state your conclusion.

b)If the average score increase is, in fact, only equal to 3 points, what type of error has the consumer group made if they fail to reject the null hypothesis (which may or may not have been your conclusion in part a)?

TYPE I     TYPE II             BOTH TYPE I and TYPE II