Final answer:
Given the z-score of 2.4 and a critical z-value of -1.645 for an alpha of 0.05, the decision for a one-tailed z-test with a lower-tail critical is to fail to reject the null hypothesis because the z-score does not fall within the rejection region.
The correct answer is option b.
Step-by-step explanation:
To determine the decision for a one-tailed z-test with a lower-tail critical at an alpha level of significance of 0.05, we compare the z-score obtained from research to the critical z-value. For an alpha level of 0.05 in a lower-tail test, the critical z-value is approximately -1.645. This means if the calculated z-score is less than -1.645, the null hypothesis should be rejected. However, if the z-score is greater than -1.645, we fail to reject the null hypothesis.
In this scenario, the researcher obtains a z-score of 2.4. Since this z-score is not less than the critical z-value of -1.645, it does not fall into the rejection region of the lower tail for an alpha of 0.05. Therefore, the correct decision is to fail to reject the null hypothesis.
It's important to note that the decision does not depend on the sample size, nor is there any need for additional information to decide as the question provides all necessary data.