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?

Answer 1

Decision is to fail to reject the null hypothesis.

Explanation:

Since our significance level is α = 0.05, but since it's a two tailed test for two proportions, in each tail, we will have 0.05/2 = 0.025.

Now, the rejection region will be the critical value at 1 - 0.025 = 0.975

From the z-table attached, the critical value at 0.975 is 1.96.

Thus, our decision rule will be;

If Z-score is less than -1.96, or greater than 1.96, we will reject the null hypothesis.

Now, we have a z-score of z = 1.946 in the question. This lies between -1.96 and 1.96.

Thus,we will fail to reject the null hypothesis