The Graduate Record Exam (GRE) is a standardized test required to be admitted to many graduate schools in the United States. A high score in GRE makes admissions more likely. According to the Educational Testing Service, the mean score for takers of GRE who do not have training courses is 555 with standard deviation of 139. Brain Philippine (BP) offers expensive GRE training courses, claiming their graduates score better than those who have not taken any training courses. To test the company's claim, a statistician
The Graduate Record Exam (GRE) is a standardized test required to be admitted to many graduate schools in the United States. A high score in GRE makes admissions more likely. According to the Educational Testing Service, the mean score for takers of GRE who do not have training courses is 555 with standard deviation of 139. Brain Philippine (BP) offers expensive GRE training courses, claiming their graduates score better than those who have not taken any training courses. To test the company's claim, a statistician randomly selected 30 graduates of BP and asked their GRE scores.
a. Formulate the appropriate null and alternative hypothesis.
b. Identify situations when Type I and Type II errors are committed and state their possible consequences.
c. Suppose the decision rule is “Reject Ho if the mean score of the sampled BP graduates is greater than 590; otherwise, accept Ho.” Compute for the level of significance for this test. Also, find the risk of concluding that the BP graduates did not score better than 555 when in fact the mean score is 600. Use 95% confidence level.
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