Question

While running a 2-sample z-test for two proportions, you find a test statistic of z=1.946. If the test is two-tailed and α=0.05, what decision will you make?

A.Reject the null.
B.Do not reject the null.
C. Not enough information to solve

Answer 1

For a two-tailed 2-sample z-test with a test statistic of z=1.946 and a significance level of α=0.05, the correct decision would be to not reject the null hypothesis as the z-value does not exceed the critical z-values of ±2.576.

Step-by-step explanation:

When running a 2-sample z-test for two proportions, and obtaining a test statistic of z=1.946 for a two-tailed test with α=0.05, we must compare the z-value to the critical z-values for this level of significance. The critical z-values for a two-tailed test at the 5% significance level (or α=0.05) are approximately ±2.576. Since the calculated z-value of 1.946 does not exceed the critical value of 2.576, the appropriate decision would be "B. Do not reject the null hypothesis." This decision is based on the rule that if the test statistic falls between the negative and positive critical values, we do not have enough evidence to reject the null hypothesis. Therefore, there's insufficient evidence to conclude that there's a significant difference between the two proportions being tested.