**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.
**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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**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

Transcribed Image Text:**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.
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