MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Educational Website Content: Understanding Hypotheses Testing in Polygraph Trials**

In a study using a polygraph machine, there were 99 results: 23 were wrong, and 76 were correct. We wish to test the claim that the polygraph results are correct less than 80% of the time using a 0.01 significance level.

**Task:**
Identify the null hypothesis, alternative hypothesis, test statistic, P-value, and any conclusions regarding the original claim. We'll approximate using a normal distribution.

**Hypotheses Options:**
1. Option A: 
   - \( H_0: p = 0.80 \)
   - \( H_1: p \neq 0.80 \)
2. Option B:
   - \( H_0: p = 0.80 \)
   - \( H_1: p < 0.80 \)
3. Option C:
   - \( H_0: p = 0.20 \)
   - \( H_1: p \neq 0.20 \)
4. Option D:
   - \( H_0: p = 0.80 \)
   - \( H_1: p > 0.80 \)
5. Option E:
   - \( H_0: p = 0.20 \)
   - \( H_1: p > 0.20 \)
6. Option F:
   - \( H_0: p = 0.20 \)
   - \( H_1: p < 0.20 \)

**Test Statistic:**
- Compute the test statistic \( z \) (Round to two decimal places).

**P-value:**
- Calculate the P-value (Round to four decimal places).

**Conclusion:**
- Determine whether there is sufficient evidence to support the claim that polygraph results are correct less than 80% of the time.

- Conclusion Statement:
  - \( \Box \) \( H_0 \): There ___ sufficient evidence to support the claim.

This setup will guide students in understanding how to apply hypothesis testing to determine the reliability of polygraph results, using a significance level to assess statistical evidence.
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Transcribed Image Text:**Educational Website Content: Understanding Hypotheses Testing in Polygraph Trials** In a study using a polygraph machine, there were 99 results: 23 were wrong, and 76 were correct. We wish to test the claim that the polygraph results are correct less than 80% of the time using a 0.01 significance level. **Task:** Identify the null hypothesis, alternative hypothesis, test statistic, P-value, and any conclusions regarding the original claim. We'll approximate using a normal distribution. **Hypotheses Options:** 1. Option A: - \( H_0: p = 0.80 \) - \( H_1: p \neq 0.80 \) 2. Option B: - \( H_0: p = 0.80 \) - \( H_1: p < 0.80 \) 3. Option C: - \( H_0: p = 0.20 \) - \( H_1: p \neq 0.20 \) 4. Option D: - \( H_0: p = 0.80 \) - \( H_1: p > 0.80 \) 5. Option E: - \( H_0: p = 0.20 \) - \( H_1: p > 0.20 \) 6. Option F: - \( H_0: p = 0.20 \) - \( H_1: p < 0.20 \) **Test Statistic:** - Compute the test statistic \( z \) (Round to two decimal places). **P-value:** - Calculate the P-value (Round to four decimal places). **Conclusion:** - Determine whether there is sufficient evidence to support the claim that polygraph results are correct less than 80% of the time. - Conclusion Statement: - \( \Box \) \( H_0 \): There ___ sufficient evidence to support the claim. This setup will guide students in understanding how to apply hypothesis testing to determine the reliability of polygraph results, using a significance level to assess statistical evidence.
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