**Hypothesis Testing for Drug Testing Accuracy** **Context:** Consider a drug testing company that provides a test for marijuana usage. Among 336 tested subjects, results from 25 subjects were found to be incorrect (either a false positive or a false negative). The aim is to test the claim that less than 10 percent of the test results are incorrect. **Objective:** Use a 0.10 significance level to evaluate whether the claim is valid. **Instructions:** 1. **Identify the Null and Alternative Hypotheses:** **Choose the correct option:** - **A.** \( H_0: p = 0.1 \) \( H_1: p < 0.1 \) - **B.** \( H_0: p < 0.1 \) \( H_1: p = 0.1 \) - **C.** \( H_0: p = 0.1 \) \( H_1: p \neq 0.1 \) - **D.** \( H_0: p = 0.1 \) \( H_1: p > 0.1 \) 2. **Tasks:** - Identify the test statistic for this hypothesis test. - Calculate this statistic, rounding to two decimal places as needed. - Identify the p-value for this hypothesis test. --- **Guide to Solving the Problem:** - **Null Hypothesis (\( H_0 \))** reflects the status quo or no effect/change scenario. In this context, it states that the proportion of incorrect results is 10%. - **Alternative Hypothesis (\( H_1 \))** represents the claim that is being tested. Here, it suggests that the proportion of incorrect results is less than 10%. - **Significance Level (Alpha = 0.10):** This is the threshold for deciding whether to reject the null hypothesis. **Testing Methodology:** - **Determine the Sample Proportion:** Calculate the proportion of incorrect results in the sample, which is 25 out of 336. - **Test Statistic Calculation:** Use the appropriate statistical formula to find the test statistic, which helps in determining the position relative to the null hypothesis. - **P-Value Determination:** This value will help decide whether to reject **Hypothesis Testing** 1. **Identify the test statistic for this hypothesis test.** - Round to two decimal places as needed. - (Field for entry) 2. **Identify the P-value for this hypothesis test.** - Round to three decimal places as needed. - (Field for entry) 3. **Identify the conclusion for this hypothesis test.** **Options:** - **A. Fail to reject \(H_0\)** There is sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong. - **B. Reject \(H_0\)** There is sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong. - **C. Fail to reject \(H_0\)** There is not sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong. - **D. Reject \(H_0\)** There is not sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong.