### Analyzing Polygraph Test Results Using Hypothesis TestingIn an educational experiment with polygraph tests, 96 trials were conducted, resulting in 24 cases of incorrect results and 72 cases of correct results. The objective is to determine if the polygraph results are accurate less than 80% of the time using hypothesis testing at a 0.01 significance level.#### Objective:To evaluate the claim that polygraph test results are correct less than 80% of the time by conducting a hypothesis test.#### Step-by-Step Procedure:1. **Define the population proportion (p):** - Let $ p $ be the population proportion of correct polygraph results.2. **Identify the Hypotheses:** - **Null Hypothesis (H₀): p = 0.80 (80% accuracy)** - **Alternative Hypothesis (H₁): p ≠ 0.80 (other than 80% accuracy)**3. **Choose the Correct Answer for Hypotheses:** - C. $ H₀: p = 0.80 $ $ H₁: p ≠ 0.80 $4. **Calculation of Test Statistic:** - The test statistic is $ z $ and is calculated as follows: \[ z = \frac{ \hat{p} - p_0 }{ \sqrt{ \frac{p_0 (1 - p_0)}{n} } } \] Where: - $ \hat{p} $ = Sample proportion of correct results = 72/96 = 0.75 - $ p_0 $ = Hypothesized proportion = 0.80 - $ n $ = Sample size = 96 Substituting the values: \[ z = \frac{ 0.75 - 0.80 }{ \sqrt{ \frac{0.80 (1 - 0.80)}{96} } } \approx -1.25 \] (Round to two decimal places as needed)5. **Determine the P-value:** - The P-value, a measure of the strength against the null hypothesis, based on the calculated $ z $-score and using standard normal distribution tables. - For $ z \approx -1.25 $, P-value

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Trials in an experiment with a polygraph include 96 results that include 24 cases of wrong results and 72 cases of correct results. Use a 0.01 significance level to test the claim that such polygraph 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. O A. H, p=0.80 H, p#0.80 O B. H p=0.20 H; p> 0.20 O C. Ho p= 0.80 O D. Ho p=0.20 H, p 0.20 O F. H p=0.80 H p<0.80 H,: p> 0.80 O E. H,: p=0.20 H,: p<0.20 The test statistic is z= (Round to two decimal places as needed.) The P-value is (Round to four decimal places as needed.) Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim. Ho. There sufficient evidence to support the claim that the polygraph results are correct less than 80% of the time,

Trials in an experiment with a polygraph include 96 results that include 24 cases of wrong results and 72 cases of correct results. Use a 0.01 significance level to test the claim that such polygraph 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. O A. H, p=0.80 H, p#0.80 O B. H p=0.20 H; p> 0.20 O C. Ho p= 0.80 O D. Ho p=0.20 H, p 0.20 O F. H p=0.80 H p<0.80 H,: p> 0.80 O E. H,: p=0.20 H,: p<0.20 The test statistic is z= (Round to two decimal places as needed.) The P-value is (Round to four decimal places as needed.) Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim. Ho. There sufficient evidence to support the claim that the polygraph results are correct less than 80% of the time,

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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