### Hypothesis Testing on Voter PreferenceSuppose you are running a study or poll about the proportion of voters who prefer Candidate A. You randomly sample 84 people and find that 43 of them match the condition you are testing.#### HypothesesYou have set up the following null and alternative hypotheses for the test you are running:- Null Hypothesis (\( H_0 \)): \( p = 0.54 \)- Alternative Hypothesis (\( H_a \)): \( p \neq 0.54 \)#### Calculate the Test StatisticTo calculate the test statistic, use the following formula for the z-score of a sample proportion:\[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}} \]where:- \( \hat{p} \) is the sample proportion- \( p_0 \) is the population proportion under the null hypothesis- \( n \) is the sample size.Given:- \( \hat{p} = \frac{43}{84} \)- \( p_0 = 0.54 \)- \( n = 84 \)Calculate the sample proportion first:\[ \hat{p} = \frac{43}{84} \approx 0.512 \]Now, calculate the standard error:\[ SE = \sqrt{\frac{p_0 (1 - p_0)}{n}} = \sqrt{\frac{0.54 \times (1 - 0.54)}{84}} = \sqrt{\frac{0.54 \times 0.46}{84}} \approx 0.054 \]Finally, compute the z-score:\[ z = \frac{0.512 - 0.54}{0.054} = \frac{-0.028}{0.054} \approx -0.519 \]So, the test statistic \( z \approx -0.519 \).This value is then used to determine the p-value and make conclusions about the hypotheses in the context of the desired significance level. Be sure to round the test statistic to 3 decimal places when reporting.### Practice This ConceptInput your calculated z-value into the provided field, and click "Submit Question" to check your understanding and compare your answers.```plaintextz = [Your Calculated z-Value]

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Question 24 <> Suppose are running a study/poll about the proportion of voters who prefer Candidate A. You randomly sample 84 people and find that 43 of them match the condition you are testing. Suppose you are have the following null and alternative hypotheses for a test you are running: Ho:p = 0.54 Ha:p # 0.54 Calculate the test statistic, rounded to 3 decimal places z = Submit Question

Question 24 <> Suppose are running a study/poll about the proportion of voters who prefer Candidate A. You randomly sample 84 people and find that 43 of them match the condition you are testing. Suppose you are have the following null and alternative hypotheses for a test you are running: Ho:p = 0.54 Ha:p # 0.54 Calculate the test statistic, rounded to 3 decimal places z = Submit Question

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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