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MATLAB: An Introduction with Applications
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 image is a step-by-step guide on how to perform a hypothesis test, specifically focusing on the claim that 92% of software engineers rate their company as a "great place to work." **Steps:** 1. **Problem Statement:** A survey of 210 randomly chosen software engineers asks if they rate the company they work for as a "great place to work." Your job is to verify this claim at a significance level of 0.10. 2. **Hypothesis Setup:** - Null Hypothesis (H₀): p = 0.92 - Alternative Hypothesis (H₁): p ≠ 0.92 3. **Standard Deviation and Test Statistic Calculation:** - Find the value of √(pq/n) and confirm that a Z-test can be used. - Use p̂ = 0.86 (sample proportion) for calculations. - Calculate standard deviation and test statistic (Z). 4. **Perform Z-test and Find P-value:** - Z-test statistic formula: \( Z = \frac{p̂ - p₀}{\sqrt{\frac{p₀(1 - p₀)}{n}}} \) - Compute the test statistic value for the given sample. - Use tables or calculators to find the p-value. 5. **Graph Explanation:** - Illustration shows a standard normal distribution curve with the critical values and the calculated test statistic. 6. **Conclusion:** - Based on the p-value, make a decision on the null hypothesis. - If p-value ≤ 0.10, reject H₀; otherwise, do not reject H₀. **Graph/Detailed Explanation:** - The graph is a bell-shaped curve representing a standard normal distribution, used to visually show the areas corresponding to the significance levels and the p-value. The mean is marked at 0, with critical regions shaded to indicate rejection areas on either side. This educational guide teaches how to set up and conduct a hypothesis test, interpret p-values, and draw conclusions based on statistical evidence.
Transcribed Image Text:The image is a step-by-step guide on how to perform a hypothesis test, specifically focusing on the claim that 92% of software engineers rate their company as a "great place to work." **Steps:** 1. **Problem Statement:** A survey of 210 randomly chosen software engineers asks if they rate the company they work for as a "great place to work." Your job is to verify this claim at a significance level of 0.10. 2. **Hypothesis Setup:** - Null Hypothesis (H₀): p = 0.92 - Alternative Hypothesis (H₁): p ≠ 0.92 3. **Standard Deviation and Test Statistic Calculation:** - Find the value of √(pq/n) and confirm that a Z-test can be used. - Use p̂ = 0.86 (sample proportion) for calculations. - Calculate standard deviation and test statistic (Z). 4. **Perform Z-test and Find P-value:** - Z-test statistic formula: \( Z = \frac{p̂ - p₀}{\sqrt{\frac{p₀(1 - p₀)}{n}}} \) - Compute the test statistic value for the given sample. - Use tables or calculators to find the p-value. 5. **Graph Explanation:** - Illustration shows a standard normal distribution curve with the critical values and the calculated test statistic. 6. **Conclusion:** - Based on the p-value, make a decision on the null hypothesis. - If p-value ≤ 0.10, reject H₀; otherwise, do not reject H₀. **Graph/Detailed Explanation:** - The graph is a bell-shaped curve representing a standard normal distribution, used to visually show the areas corresponding to the significance levels and the p-value. The mean is marked at 0, with critical regions shaded to indicate rejection areas on either side. This educational guide teaches how to set up and conduct a hypothesis test, interpret p-values, and draw conclusions based on statistical evidence.
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