Question: Suppose that you are trying to compare two populations on some variable (GMAT scores of men versus women, for example). Specifically, you are testing the null hypothesis that the means of the two populations are equal versus a two-tailed hypothesis. Are the following statements correct? Why or why not?
a. A given difference (such as five points) between sample means from these populations will probably not be considered statistically significant if the sample sizes are small, but it will probably be considered statistically significant if the sample sizes are large.
b. Virtually any difference between the population means will lead to statistically significant sample results if the sample sizes are sufficiently large.