Use α to find the critical value(s), then determine if the given test statistic is in the rejection region.
$\left(A\right)$ $H_0:\mu =7.5$; $H_a:\mu >7.5$
$\alpha =0.01;z=2.17$

• A. Test is TWO-tailed, Critical value(s): $\pm 2.33$, Test stat IN rejection region.
• B. Test is LEFT-tailed, Critical value(s): $-2.33$, Test stat NOT IN rejection region.
• C. Test is RIGHT-tailed, Critical value(s): $2.33$, Test stat NOT IN rejection region.
• D. Test is RIGHT-tailed, Critical value(s): $2.17$, Test stat IN rejection region.

Answer: (C)

Verified step by step guidance

1. Identify the type of hypothesis test based on the alternative hypothesis \(H_a\). Since \(H_a: \mu > 7.5\), this is a right-tailed test.
2. Determine the critical value for the given significance level \(\alpha = 0.01\) in a right-tailed test. This critical value corresponds to the z-score where the area to the right is 0.01.
3. Use a z-table or statistical software to find the critical z-value for \(\alpha = 0.01\) in the right tail. This value is typically around 2.33.
4. Compare the test statistic \(z = 2.17\) to the critical value \(z_{critical} = 2.33\). If the test statistic is greater than the critical value, it falls in the rejection region.
5. Since \$2.17\( is less than \)2.33$, the test statistic is NOT in the rejection region, so we fail to reject the null hypothesis at the 0.01 significance level.