Question: 3. Testing for Differences in Two Populations: Means (Equal Variances). Referring to the data obtained in both preceding questions, consider testing whether the two populations

3. Testing for Differences in Two Populations: Means

(Equal Variances).

Referring to the data obtained in both preceding questions, consider testing whether the two populations means are the same. Assume that the population variances are identical in the two cases–did you find any evidence to contradict this in your answer to (2) above?

(a) Define a GLR size .05 test of the H0: m1 m2 versus Ha: not H0, where m1 and m2 refer to the means of the populations from which the first and second sample were taken. Test the hypothesis.

(b) Repeat

(a) for the hypothesis H0: m1 m2 versus Ha:

not H0.

(c) Define a GLR size .05 test of the H0: m1 ¼ m2 versus Ha: not H0 . Test the hypothesis at the .10 level of significance.

(d) Define the power function for each of the hypothesis testing procedures you defined above. With the aid of a computer, plot the power functions and interpret their meanings.

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