One-Tailed Hypothesis Test

Explanation

This is a one tailed test and the z-value of -2.33 suggests that it is a lower tailed test and that it is for a 1% level of significance.

To answer this question, we need to understand the concepts of critical values and one-tailed hypothesis tests.

In a hypothesis test, we start with a null hypothesis (H₀) and an alternative hypothesis (H₁). The null hypothesis represents the default or no-effect scenario, while the alternative hypothesis represents the scenario we are trying to prove or support.

A one-tailed hypothesis test is used when we are only interested in detecting an effect in one direction (either positive or negative), rather than both directions. In this case, the critical value represents the threshold at which we reject the null hypothesis in favor of the alternative hypothesis.

The critical value is determined based on the chosen significance level, denoted as alpha (α). The significance level represents the maximum probability of making a Type I error, which is the probability of rejecting the null hypothesis when it is true. Commonly used significance levels are 0.05 (5%) and 0.01 (1%).

Now, let's analyze the given information:

The critical value of the test statistic is -2.33. Since it is mentioned that this is a one-tailed hypothesis test, we can infer that the test is either an upper-tailed test (where we are interested in detecting an effect in the positive direction) or a lower-tailed test (where we are interested in detecting an effect in the negative direction).

For an upper-tailed test, the critical value would be positive, indicating that we reject the null hypothesis if the test statistic is greater than the critical value. However, in this case, the critical value is negative (-2.33), which suggests that it corresponds to a lower-tailed test.

Now, we need to determine the significance level (alpha) associated with this critical value. Since the question provides multiple choices for alpha, we can assess each one:

A. alpha = .05 for a lower-tailed test: This choice suggests that the significance level is 0.05 (5%) for a lower-tailed test. However, since the critical value is -2.33, which corresponds to a lower-tailed test, the significance level associated with this critical value is not 0.05.

B. alpha = .01 for an upper-tailed test: This choice suggests that the significance level is 0.01 (1%) for an upper-tailed test. As discussed earlier, the critical value of -2.33 corresponds to a lower-tailed test, not an upper-tailed test. Therefore, this choice is incorrect.

C. alpha = .05 for an upper-tailed test: This choice suggests that the significance level is 0.05 (5%) for an upper-tailed test. However, as we concluded earlier, the critical value of -2.33 corresponds to a lower-tailed test, not an upper-tailed test. Therefore, this choice is incorrect.

D. alpha = .01 for a lower-tailed test: This choice suggests that the significance level is 0.01 (1%) for a lower-tailed test. Since the critical value of -2.33 corresponds to a lower-tailed test, this choice aligns with the given information. Therefore, this is the correct answer.

E. none of these answers: This choice can be eliminated because we have found a valid answer in choice D.

In summary, based on the given information, the correct answer is:

D. alpha = .01 for a lower-tailed test.