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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 GMAT by an average of 30 points. A consumer group wishes to test if the average score increase is less than 30 points. Assume the population distribution of increase in GMAT scores is approximately Normal. a) What are the hypotheses the consumer group wishes to test? b) A simple random sample is taken of 15 students who took the course and the GMAT again. The average increase of the GMAT scores in the sample was 26 with a standard deviation of 5.4. What is the value of the test statistic? c) What can we say about the value of the P-value? Is the result statistically significant at 5% level? d) Could the consumer group make a Type II error? Explain. e) Assume the standard deviation for the distribution of increase in GMAT scores is or: 5. At the 5% significance level, what is the power ofthe test when, in fact, y: 26