mals in an experiment with pory polygrap results are correct less than 80% of the time. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution. Let p be the population proportion of correct polygraph results. Identify the null and alternative hypotheses. Choose the correct answer below. 4 OB. Ho p=0.20 H₁ p *0.20 OA. Ho: P=0.20 H₁: p>0.20 OC. Ho: p=0.80 H₁: p<0.80 OE. Ho: p=0.20 H₁: p<0.20 The test statistic is z= (Round to two decimal places as needed.) OD. Ho p=0.80 H₁: p*0.80 OF. Ho p=0.80 H₁: p>0.80
mals in an experiment with pory polygrap results are correct less than 80% of the time. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution. Let p be the population proportion of correct polygraph results. Identify the null and alternative hypotheses. Choose the correct answer below. 4 OB. Ho p=0.20 H₁ p *0.20 OA. Ho: P=0.20 H₁: p>0.20 OC. Ho: p=0.80 H₁: p<0.80 OE. Ho: p=0.20 H₁: p<0.20 The test statistic is z= (Round to two decimal places as needed.) OD. Ho p=0.80 H₁: p*0.80 OF. Ho p=0.80 H₁: p>0.80
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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![**Transcription for Educational Use:**
In an experiment with a polygraph, there are 97 results, including 24 cases of wrong results and 73 cases of correct results. A significance level of 0.05 is used to test the claim that such polygraph results are correct less than 80% of the time. The task is to identify the null hypothesis, alternative hypothesis, test statistic, P-value, and conclusion about the null hypothesis and the final conclusion that addresses the original claim. The P-value method is used, and the normal distribution is applied as an approximation of the binomial distribution.
**Hypotheses Options:**
- A. \( H_0: p = 0.80 \)
\( H_1: p < 0.80 \)
- B. \( H_0: p = 0.80 \)
\( H_1: p \neq 0.80 \)
- C. \( H_0: p = 0.80 \)
\( H_1: p > 0.80 \)
- D. \( H_0: p = 0.80 \)
\( H_1: p \geq 0.80 \)
- E. \( H_0: p = 0.20 \)
\( H_1: p < 0.20 \)
- F. \( H_0: p = 0.80 \)
\( H_1: p > 0.80 \)
**Calculations:**
- **The test statistic is:**
\( Z = \_\_ \) (Round to two decimal places as needed.)
- **The P-value is:**
\_\_ (Round to four decimal places as needed.)
**Conclusion:**
Identify whether there is sufficient evidence to support the claim that the polygraph results are correct less than 80% of the time. Indicate this by choosing:
[Dropdown: Reject \( H_0 \) / Fail to reject \( H_0 \)]
There \_\_\_ sufficient evidence to support the claim that the polygraph results are correct less than 80% of the time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c582252-6541-4096-9706-b4f3b52fcf1c%2F32e9e77b-1234-4c8e-bc8a-8a5600511597%2Fe4t5s3d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Use:**
In an experiment with a polygraph, there are 97 results, including 24 cases of wrong results and 73 cases of correct results. A significance level of 0.05 is used to test the claim that such polygraph results are correct less than 80% of the time. The task is to identify the null hypothesis, alternative hypothesis, test statistic, P-value, and conclusion about the null hypothesis and the final conclusion that addresses the original claim. The P-value method is used, and the normal distribution is applied as an approximation of the binomial distribution.
**Hypotheses Options:**
- A. \( H_0: p = 0.80 \)
\( H_1: p < 0.80 \)
- B. \( H_0: p = 0.80 \)
\( H_1: p \neq 0.80 \)
- C. \( H_0: p = 0.80 \)
\( H_1: p > 0.80 \)
- D. \( H_0: p = 0.80 \)
\( H_1: p \geq 0.80 \)
- E. \( H_0: p = 0.20 \)
\( H_1: p < 0.20 \)
- F. \( H_0: p = 0.80 \)
\( H_1: p > 0.80 \)
**Calculations:**
- **The test statistic is:**
\( Z = \_\_ \) (Round to two decimal places as needed.)
- **The P-value is:**
\_\_ (Round to four decimal places as needed.)
**Conclusion:**
Identify whether there is sufficient evidence to support the claim that the polygraph results are correct less than 80% of the time. Indicate this by choosing:
[Dropdown: Reject \( H_0 \) / Fail to reject \( H_0 \)]
There \_\_\_ sufficient evidence to support the claim that the polygraph results are correct less than 80% of the time.
Transcribed Image Text:### Investigation of Polygraph Accuracy
**Context:**
In a study involving polygraph tests, 97 trials yielded 24 incorrect results and 73 correct results. The objective is to test, at a 0.05 significance level, whether the polygraph results are accurate less than 80% of the time.
**Task:**
Identify the null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_1\)). Use the normal distribution to approximate the binomial distribution and determine the test statistic, P-value, and conclusion regarding the original claim.
#### Hypothesis Options:
- \( \text{Option A:} \)
- \( H_0: p = 0.20 \)
- \( H_1: p > 0.20 \)
- \( \text{Option B:} \)
- \( H_0: p = 0.20 \)
- \( H_1: p \neq 0.20 \)
- \( \text{Option C:} \)
- \( H_0: p = 0.80 \)
- \( H_1: p < 0.80 \)
- \( \text{Option D:} \)
- \( H_0: p = 0.80 \)
- \( H_1: p \neq 0.80 \)
- \( \text{Option E:} \)
- \( H_0: p = 0.20 \)
- \( H_1: p < 0.20 \)
- \( \text{Option F:} \)
- \( H_0: p = 0.80 \)
- \( H_1: p > 0.80 \)
**Test Statistic Calculation:**
- Round the test statistic \( z \) to two decimal places as needed.
*Note: The question prompt implies the correct hypotheses test whether the proportion \( p \) of correct results is less than 0.80, suggesting Option C is relevant.*
This scenario introduces hypothesis testing using a polygraph test context to determine accuracy levels through statistical analysis.
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