Consider a drug testing company that provides a test for marijuana usage. Among 294 tested subjects, results from 29 subjects were wrong (either a false positive or a false negative). Use a 0.05 significance level to test the claim that less than 10 percent of the test results are wrong. OD. Ho: p=0.1 H₁: p *0.1 Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is (Round to two decimal places as needed.) Identify the P-value for this hypothesis test. The P-value for this hypothesis test is (Round to three decimal places as needed.) Identify the conclusion for this hypothesis test. O A. Reject Ho. There is sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong. OB. Fail to reject Ho. There is not sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong. OC. Reject Ho. There is not sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong. OD. Fail to reject Ho. There is sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong.
Consider a drug testing company that provides a test for marijuana usage. Among 294 tested subjects, results from 29 subjects were wrong (either a false positive or a false negative). Use a 0.05 significance level to test the claim that less than 10 percent of the test results are wrong. OD. Ho: p=0.1 H₁: p *0.1 Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is (Round to two decimal places as needed.) Identify the P-value for this hypothesis test. The P-value for this hypothesis test is (Round to three decimal places as needed.) Identify the conclusion for this hypothesis test. O A. Reject Ho. There is sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong. OB. Fail to reject Ho. There is not sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong. OC. Reject Ho. There is not sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong. OD. Fail to reject Ho. There is sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong.
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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![### Hypothesis Testing for Accuracy of Drug Tests
Consider a drug testing company that provides a test for marijuana usage. Among 294 tested subjects, results from 29 subjects were wrong (either a false positive or a false negative). We will use a 0.05 significance level to test the claim that less than 10 percent of the test results are wrong.
#### Hypotheses:
\[
\begin{aligned}
&\text{Null Hypothesis (H}_0\text{): } p = 0.1 \\
&\text{Alternative Hypothesis (H}_1\text{): } p \neq 0.1
\end{aligned}
\]
### Step-by-Step Solution:
1. **Identify the Test Statistic for this Hypothesis Test:**
- The test statistic for this hypothesis test is \( Z \).
- To calculate the test statistic, you may use the formula for a proportion test:
\[
Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}
\]
where:
- \(\hat{p}\) = sample proportion (29/294)
- \(p_0\) = hypothesized proportion (0.1)
- \(n\) = sample size (294)
(Round to two decimal places as needed.)
2. **Identify the P-value for this Hypothesis Test:**
- Calculate the P-value using the Z-test statistic obtained.
- Use statistical tables or software to determine the P-value from the Z value.
(Round to three decimal places as needed.)
3. **Conclusion:**
- Based on the P-value obtained, compare it to the significance level (\(\alpha = 0.05\)):
- If \( P \leq \alpha \), reject the null hypothesis (\(H_0\)).
- If \( P > \alpha \), fail to reject the null hypothesis (\(H_0\)).
### Possible Conclusions:
- **Option A:** Reject \( H_0 \). There is sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong.
- **Option B:** 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4cbada35-3122-4a6c-a25c-246bca0ae236%2Ff73fa2b3-17df-49b0-bbdb-26a2ebf8e283%2Fq8e89fb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for Accuracy of Drug Tests
Consider a drug testing company that provides a test for marijuana usage. Among 294 tested subjects, results from 29 subjects were wrong (either a false positive or a false negative). We will use a 0.05 significance level to test the claim that less than 10 percent of the test results are wrong.
#### Hypotheses:
\[
\begin{aligned}
&\text{Null Hypothesis (H}_0\text{): } p = 0.1 \\
&\text{Alternative Hypothesis (H}_1\text{): } p \neq 0.1
\end{aligned}
\]
### Step-by-Step Solution:
1. **Identify the Test Statistic for this Hypothesis Test:**
- The test statistic for this hypothesis test is \( Z \).
- To calculate the test statistic, you may use the formula for a proportion test:
\[
Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}
\]
where:
- \(\hat{p}\) = sample proportion (29/294)
- \(p_0\) = hypothesized proportion (0.1)
- \(n\) = sample size (294)
(Round to two decimal places as needed.)
2. **Identify the P-value for this Hypothesis Test:**
- Calculate the P-value using the Z-test statistic obtained.
- Use statistical tables or software to determine the P-value from the Z value.
(Round to three decimal places as needed.)
3. **Conclusion:**
- Based on the P-value obtained, compare it to the significance level (\(\alpha = 0.05\)):
- If \( P \leq \alpha \), reject the null hypothesis (\(H_0\)).
- If \( P > \alpha \), fail to reject the null hypothesis (\(H_0\)).
### Possible Conclusions:
- **Option A:** Reject \( H_0 \). There is sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong.
- **Option B:** 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
Transcribed Image Text:### Hypothesis Testing: Marijuana Usage Test
#### Problem Statement
Consider a drug testing company that provides a test for marijuana usage. Among 294 tested subjects, results from 29 subjects were wrong (either a false positive or a false negative). Use a 0.05 significance level to test the claim that less than 10 percent of the test results are wrong.
#### Hypothesis Identification
Identify the null and alternative hypotheses for this test. Choose the correct answer below.
- **A.** \( H_0: p = 0.1 \)
\( H_1: p < 0.1 \)
- **B.** \( H_0: p < 0.1 \)
\( H_1: p = 0.1 \)
- **C.** \( H_0: p = 0.1 \)
\( H_1: p > 0.1 \)
- **D.** \( H_0: p = 0.1 \)
\( H_1: p \neq 0.1 \)
#### Hypothesis Test Computations
1. **Identify the Test Statistic for this Hypothesis Test**
The test statistic for this hypothesis test is \( \quad \boxed{ } \)
(Round to two decimal places as needed.)
2. **Identify the P-value for this Hypothesis Test**
The P-value for this hypothesis test is \( \quad \boxed{ } \)
(Round to three decimal places as needed.)
3. **Identify the Conclusion for this Hypothesis Test**
Based on the computations and the significance level, determine whether to reject or fail to reject the null hypothesis.
---
This excerpt is an exercise in hypothesis testing, often found in introductory statistics courses. Ensure that the calculations and hypotheses are verified correctly for educational accuracy.
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