# Hypothesis Testing for a Marriage Counselor's ProgramA marriage counselor has traditionally observed that the proportion \( p \) of all married couples for whom her communication program can prevent divorce is 77%. After implementing some recent changes, the marriage counselor claims that her program can prevent divorce in more than 77% of married couples. In a random sample of 250 married couples who completed her program, 194 of them stayed together. Based on this sample, is there enough evidence to support the marriage counselor's claim at the 0.10 level of significance?## Steps to Perform a One-Tailed Test1. **State the Hypotheses:** - **Null Hypothesis (\( H_0 \)):** \( p = 0.77 \) - **Alternative Hypothesis (\( H_1 \)):** \( p > 0.77 \)2. **Determine the Test Statistic:** - Choose an appropriate test statistic (not specified in the image, but likely a z-test for proportions due to sample size).3. **Compute the Test Statistic:** - Calculate using the sample data. (Round to three or more decimal places; computations not provided in the image).4. **Find the p-value:** - Determine the p-value associated with the test statistic. (Round to three or more decimal places; computations not provided in the image).5. **Conclusion:** - Decide if there is enough evidence to support the marriage counselor's claim based on the p-value and the level of significance (0.10). - Options for answering: Yes or No.### Visual Aids- **Symbols and buttons:** - Various statistical symbols \( \mu, \sigma, p \) and others might be useful for calculations but are not labeled with specific values or data in the image. The provided data and methods guide one to apply hypothesis testing to assess the effectiveness of the counselor's revised program.

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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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The dataset "nurses" is a random sample of 1,000 cases from “Health Care Provider Credential Data” from Washington State Open Data Portal. In the sample, there are 418 CNA's and 278 of the CNA's have expired credentials. Use the statistics from the nurses dataset to answer the following question: "With 90% confidence, what percent of all CNA's on Washington State's healthcare provider list are expired?"
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