Problem

Find the critical value(s) and rejection region(s) for the type of z-test with level of significance $\alpha$. Include a graph with your answer. Right-tailed test, $\alpha=0.02$ The critical value(s) is/are $z=2.05$. (Round to two decimal places as needed. Use a comma to separate answers as needed.) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Round to two decimal places as needed.) A. The rejection regions are $\mathrm{z}<\square$ and $\mathrm{z}>\square$. B. The rejection region is $z<\square$. C. The rejection region is $z>\square$.

Solution

Step 1 :This is a right-tailed test, which means we are looking for values that are greater than a certain threshold. The level of significance, \(\alpha\), is the probability of rejecting the null hypothesis when it is true. In this case, \(\alpha=0.02\).

Step 2 :The critical value is the value of the test statistic that separates the region where we would reject the null hypothesis from the region where we would not. We can find this value using a standard normal distribution table or a z-score calculator.

Step 3 :The rejection region is the range of values for which we would reject the null hypothesis. For a right-tailed test, this is all values greater than the critical value.

Step 4 :Given that the critical value is 2.05, this means that for a right-tailed test, we would reject the null hypothesis for any z-score greater than 2.05.

Step 5 :Final Answer: The rejection region is \(z>2.05\). Therefore, the correct choice is C. The rejection region is \(z>\boxed{2.05}\).

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