Which of the following graphs best represents the rejection region for the hypothesis test with null hypothesis $H_0:p\le 8.1$?

• A. A left-tailed test, where the rejection region is in the lower tail of the distribution (values of $p$ less than $8.1$)
• B. A right-tailed test, where the rejection region is in the upper tail of the distribution (values of $p$ greater than $8.1$)
• C. A two-tailed test, where the rejection regions are in both tails of the distribution
• D.

Answer: (B)

Verified step by step guidance

1. Identify the null hypothesis (H0) and the alternative hypothesis (Ha). Here, H0: p \leq 8.1, which means the parameter p is less than or equal to 8.1. The alternative hypothesis Ha would be p > 8.1, since the test is checking if p is greater than 8.1.
2. Determine the type of test based on the alternative hypothesis. Since Ha states p > 8.1, this indicates a right-tailed test because we are interested in values of p greater than 8.1.
3. Understand the rejection region for a right-tailed test. The rejection region is located in the upper tail of the sampling distribution, corresponding to values of the test statistic that are significantly greater than the hypothesized value under H0.
4. Visualize the rejection region on the graph. For a right-tailed test, the rejection region will be on the right side (upper tail) of the distribution curve, representing values of p greater than 8.1.
5. Conclude that the correct graph is the one showing the rejection region in the upper tail, matching the alternative hypothesis p > 8.1, which corresponds to a right-tailed test.