A researcher has two independent samples from two populations A and B. Her null

Question

A researcher has two independent samples from two populations A and B. Her null hypothesis is that the population averages are the same. She performs a z-test, using the z-score of the difference of the sample averages (average(A) - average(B)) as her test statistic. The value of the statistic is about 1.8. This difference is statistically significant if her alternative hypothesis is:

a. the population avergage of A is differnt from the population average of B

b. it will be statistically significant for neither of the above alternative hypotheses

c. the population average of A is greater than the population aberage of B

d. it will be statistically significant for either of the baove alternative hypotheses

Explanation / Answer

The value of the test statistic is about 1.8.

The Null hypothesis is that the population averages are the same.

For a 2-tailed test of the hypothesis, the 5% level of significance corresponds to a critical value of 1.96 and for a one-tailed test, the critical value is 1.645.

Since our test statistic is 1.8, it is greater than the critical value of 1.645 for a one-tailed test, but less than the critical value of 1.96 for a 2-tailed test.

So, for a one-tailed test, we can reject the Null hypothesis, but for 2-tailed test, we cannot reject the Null hypothesis.

So the test statistic is statistically significant for a one-tailed test (for which the alternate hypothesis is that the population average of A is greater than the population average of B), whereas the test statistic is not statistically significant for a 2-tailed test (for which the alternate hypothesis is that the population average of A is different from the population average average of B).

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.