## Hypothesis Testing for Proportion of Couples in a Communication ProgramA marriage counselor claims that her communication program can prevent divorce in more than 80% of married couples. She recently tested this claim with a sample of 220 married couples, finding that 192 stayed together. We will test her claim at the 0.10 level of significance.### Steps to Perform the Test:(a) **State the Null and Alternative Hypotheses:**- Null Hypothesis (\(H_0\)): \(p = 0.8\)- Alternative Hypothesis (\(H_1\)): \(p > 0.8\)(b) **Determine the Type of Test Statistic:**Choose a **z-test** for proportions as the test statistic.(c) **Find the Test Statistic Value:**Calculate the z-score by using the formula:\[z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}\]Where:- \(\hat{p} = \frac{192}{220}\)- \(p_0 = 0.8\)- \(n = 220\)(d) **Find the Critical Value:**For a one-tailed test at the 0.10 level of significance, the critical z-value is approximately 1.28.(e) **Decision:**Compare the calculated z-value to the critical value to determine if there is sufficient evidence to support the counselor’s claim.### Summary:Evaluate whether the evidence supports the claim that more than 80% of couples in the program stay together by comparing the test statistic to the critical value. If the test statistic exceeds the critical value, conclude there is sufficient evidence to reject the null hypothesis in favor of the alternative.

A marriage counselor has traditionally seen that the proportion p of all married couples for whom her communication program can prevent divorce is making some recent changes, the marriage counselor now claims that her program can prevent divorce in more than 80% of married couples. In a ra sample of 220 married couples who completed her program, 192 of them stayed together. Based on this sample, is there enough evidence to support marriage counselor's claim at the 0.10 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. H:0 H₁ :0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) 3 Ix 09 a 00 S 00 0=0 OSO OD

A marriage counselor has traditionally seen that the proportion p of all married couples for whom her communication program can prevent divorce is making some recent changes, the marriage counselor now claims that her program can prevent divorce in more than 80% of married couples. In a ra sample of 220 married couples who completed her program, 192 of them stayed together. Based on this sample, is there enough evidence to support marriage counselor's claim at the 0.10 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. H:0 H₁ :0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) 3 Ix 09 a 00 S 00 0=0 OSO OD

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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