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.

Pretend the ETS revises the current GRE test (the one with an average score of 302.60), but without stating whether they predict it to be easier or more difficult than the current GRE. All they hypothesize that the changed GRE test will result in a significantly different GRE average than the current GRE test.

Question #6: State the two-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 #7:If ETS tests this revised GRE on a sample of 400 students, and find an average of 303.45, what is the Z_obt of this sample?

Question #8: Again, ETS hypothesizes that the revised GRE test will result in a significantly different average GRE score than the current GRE test. What is(are) the Z_crit (s) for testing of this hypothesis, assuming an alpha of 0.05.

Question #9:Did the revised GRE test result in a significantly different average GRE score? Explain how you came to your conclusion.

Question #10: Let’s say that, despite what our statistics say, in nature (or in reality) the revised GRE test produces an average that is different than the current GRE test. What type of error would we say occurred in ETS’s study on the revised GRE test?

Answer 1

6] NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS HA

7]

8] Zcritical value= 1.96

9] Since Z obtained SMALLER THAN THE Z critical value therefore NOT SIGNIFICANT.

DECISION: DO NOT REJECT H0.

Conclusion: We do not have sufficient evidence to conclude that the poplation mean is different than 302.6

10] TYPE 2 ERROR: RETAINING H0 WHEN IT IS FALSE.