### Educational Website Transcription: Statistical Hypothesis Testing Example**Topic: Hypothesis Testing for Proportions****Example Scenario:**A presidential candidate’s aide estimates that, among all college students, the proportion \( p \) who intend to vote in the upcoming election is at least 60%. If 129 out of a random sample of 230 college students expressed an intent to vote, can we reject the aide’s estimate at the 0.05 level of significance?### Steps to Perform a One-Tailed TestCarry your intermediate computations to three or more decimal places and round your answers as specified below. (If necessary, consult a list of formulas.)#### (a) State the hypotheses:- **Null Hypothesis (\( H_0 \))**: \( p = 0.60 \)- **Alternative Hypothesis (\( H_1 \))**: \( p < 0.60 \)This represents a one-tailed test where we are testing if the proportion is less than 60%.#### (b) Determine the type of test statistic to use:*Choose one from:*- Z (for large sample size and proportion)- T (for smaller sample size or unknown population standard deviation)- Chi-square- FFor this scenario, we use the **Z-test** since we are dealing with proportions and have a sufficiently large sample size.#### (c) Find the value of the test statistic:Substitute the given values into the Z-test formula for proportions. Here, the formula is:\[ Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}} \]Where:- \(\hat{p}\) = sample proportion = \(\frac{129}{230}\)- \(p_0\) = hypothesized population proportion = 0.60- \(n\) = sample size = 230Calculate the sample proportion:\[ \hat{p} = \frac{129}{230} = 0.561 \]Calculate the standard error:\[ SE = \sqrt{\frac{0.60 \times 0.40}{230}} = 0.0324 \]Calculate the Z value:\[ Z = \frac{0.561 - 0.60}{0.0324} = -1.2037 \]Round off the answer to

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A presidential candidate's aide estimates that, among all college students, the proportion p who intend to vote in the upcoming election is at least 60%. out of a random sample of 230 college students expressed an intent to vote, can we reject the aide's estimate at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (if necessary, consult a listof fermulas-) (0) state the null hypothesis H, and the alternative hypothesis Hq- (b) Determine the type of test statistic to use. (Choose one) D-O Oso D20 (e) Find the value of the test statistic. (Round to three or more decimal places.) ? (4) Find the p-value. (Round to three or more decimal places.) (e) Can we reject the aide's estimate that the proportion of college students who intend to vote is at least 60?

A presidential candidate's aide estimates that, among all college students, the proportion p who intend to vote in the upcoming election is at least 60%. out of a random sample of 230 college students expressed an intent to vote, can we reject the aide's estimate at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (if necessary, consult a listof fermulas-) (0) state the null hypothesis H, and the alternative hypothesis Hq- (b) Determine the type of test statistic to use. (Choose one) D-O Oso D20 (e) Find the value of the test statistic. (Round to three or more decimal places.) ? (4) Find the p-value. (Round to three or more decimal places.) (e) Can we reject the aide's estimate that the proportion of college students who intend to vote is at least 60?

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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