Questions: Find the critical value(s) and rejection region(s) for the type of z-test with level of significance α. Include a graph with your answer. Right-tailed test, α=0.08 The critical value(s) is/are z= (Round to two decimal places as needed. Use a comma to separate answers as needed.)

Solution Steps

We are tasked with finding the critical value(s) and rejection region(s) for a right-tailed z-test with a level of significance \(\alpha = 0.08\). A right-tailed test means we are looking for the critical value where the area to the right under the standard normal distribution curve is 0.08.

For a right-tailed test, the critical value \(z\) is the z-score that corresponds to the cumulative probability of \(1 - \alpha\). Here, \(\alpha = 0.08\), so we need to find the z-score for a cumulative probability of \(1 - 0.08 = 0.92\).

Using a standard normal distribution table or a calculator, we find the z-score that corresponds to a cumulative probability of 0.92.

The z-score for a cumulative probability of 0.92 is approximately 1.41. This means that the critical value for this right-tailed test is \(z = 1.41\).

For a right-tailed test, the rejection region is the area to the right of the critical value. Therefore, the rejection region is \(z > 1.41\).

To visualize this, we can draw a standard normal distribution curve and shade the area to the right of \(z = 1.41\). This shaded area represents the rejection region.

Final Answer