Answer :
In the scenario where the calculated Z score is exactly equal to the critical Z value at ±1.64 for a two-tailed test, the decision is to fail to reject the null hypothesis.
If the calculated Z score for a two-tailed test is 1.64 and the Z critical value is ±1.64, our decision-making process would look at whether the calculated Z falls within the rejection region or not. Since the calculated Z is equal to the critical Z, it lies exactly on the threshold. In traditional hypothesis testing, we would not reject the null hypothesis (H0) if the test statistic does not fall into the rejection region (which would be beyond ±1.64 in this case). Thus, in this specific scenario, the conclusion is to fail to reject the null hypothesis, because the calculated Z score is not beyond the critical value in either tail of the distribution.
