Question: (16 points) Score-S-Up is a company that helps students improve 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 the 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 the sample was 3.7.

1. Perform a hypothesis test with significance level 5%. Show all work, and clearly state your conclusion.
2. 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? (Circle or underline one of the following.)

TYPE I TYPE II BOTH TYPE I and TYPE II

Price: $2.99

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