### Hypothesis Testing for Proportion of Voters Preferring Candidate A**Problem Statement:**You are conducting a study to determine if the proportion of voters who prefer Candidate A is significantly more than 0.16. You are using a significance level of \(\alpha = 0.01\).**Hypotheses:**- \(H_0\): \(p = 0.16\)- \(H_1\): \(p > 0.16\)**Sample Data:**- Sample size (\(n\)) = 621- Number of successes (voters preferring Candidate A) = 104**Tasks:**1. **Calculate the Test Statistic:** - Formula for the test statistic (z) for proportions: \[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} \] - Where: - \(\hat{p}\) = sample proportion = \(\frac{104}{621}\) - \(p_0\) = hypothesized population proportion = 0.16 - Substitute in the appropriate values and calculate the test statistic. Report the answer accurate to three decimal places.2. **Determine the p-value:** - The p-value is the probability that the observed sample proportion would be as extreme or more extreme than what was observed, given that the null hypothesis is true. - Use standard normal distribution tables or software to find the p-value corresponding to the calculated test statistic. - Report the p-value accurate to four decimal places.3. **Comparison with Significance Level (\(\alpha\)):** - The p-value is either: - less than (or equal to) \(\alpha\) - greater than \(\alpha\)4. **Decision on Null Hypothesis:** - Based on the p-value and the significance level (\(\alpha\)), decide whether to: - reject the null hypothesis - accept the null hypothesis - fail to reject the null hypothesis5. **Final Conclusion:** - Analyze the context and make a conclusion regarding the claim. Possible conclusions: - There is sufficient evidence to warrant rejection of the claim that the proportion of voters who prefer Candidate A is more than 0.16. - There is not sufficient evidence to warrant

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You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly more than 0.16. You use a significance level of a = 0.01. Ho:p = 0.16 H1:p > 0.16 You obtain a sample of size n 621 in which there are 104 successes. %3D

You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly more than 0.16. You use a significance level of a = 0.01. Ho:p = 0.16 H1:p > 0.16 You obtain a sample of size n 621 in which there are 104 successes. %3D

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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