Question

BACKGROUND: According to the Educational Testing Service (ETS), the national average on the Graduate Record Examinations (GRE), a standardized test that is an admissions requirement for most graduate schools in the United States, is 302.60 (with the verbal and quantitative subsections combined). Unfortunately, ETS does not provide a standard deviation for total GRE score (only standard deviations for the two subsections), so let’s just use a standard deviation of 12.

PROBLEM (FICTIONAL): ETS has received number complaints from universities that the current GRE does not provide a valid measure of a student’s quality (i.e., capability to succeed in graduate school). Indeed, many universities feel that the current GRE is too easy compared to previous versions, and thus more students who are not capable of succeeding in graduate school are receiving scores that suggest otherwise. Thus, beginning in 2019, ETS is making the GRE more difficult, which should lower the average GRE score of future GRE takers.

Answer the below questions (each worth 2 pts):

Question #1: ETS hypothesizes that the new, more difficult GRE test will result in a significantly lower average GRE score than the current GRE test. State the one-tailed alternative and null hypotheses (using the new statistical notation for stating mathematical relationships found on page 207) that would be used in testing this hypothesis.

Question #2: Again, ETS hypothesizes that the new, more difficult GRE test will result in a significantly lower average GRE score than the current GRE test. What is the Zcrit for testing of this hypothesis, assuming an alpha of 0.05.

In order to test whether or not the new, more difficult GRE test significantly lowered the average GRE score, ETS administered it to a sample of 225 students. The average GRE score of this sample was 301.25. With this information, answer the following questions:

Question #3: What is Zobt for the sample mean of the 225 students who took the new, more difficult GRE test (round to two decimal places)?

Question #4: Did the new, more difficult GRE result in a significantly lower average GRE score? Explain how you came to your conclusion.

Question #5: Let’s say that, despite what our statistics say, in nature (or in reality) the new, more difficult GRE test is actually no more difficult on average than the current GRE test. What type of error would we say occurred in ETS’s study on the new, more difficult GRE test?

Answer 1