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b. Suppose that a sample of n = 400 students at the same university (instead of n = 100) determines that 25% of the sample use the web browser. At the 0.05 level of significance, there evidence that the market share for the web browser at the university is greater than the worldwide market share of 20.4%? Calculate the test statistic for the second sample. ZSTAT (Type an integer or a decimal. Round to two decimal places as needed.)

b. Suppose that a sample of n = 400 students at the same university (instead of n = 100) determines that 25% of the sample use the web browser. At the 0.05 level of significance, there evidence that the market share for the web browser at the university is greater than the worldwide market share of 20.4%? Calculate the test statistic for the second sample. ZSTAT (Type an integer or a decimal. Round to two decimal places as needed.)

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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**Hypothesis Testing Example** The worldwide market share for a particular web browser was 20.4% in a recent month. A sample of 100 random students at a certain university finds that 25 use this browser. We will complete parts (a) through (b) below. **Part (a):** - **Task:** Calculate the test statistic to determine if there is evidence that the market share at the university is different from 20.4%. 1. **Hypotheses:** - Null hypothesis (\(H_0\)): \(\pi = 0.204\) - Alternative hypothesis (\(H_1\)): \(\pi > 0.204\) 2. **Calculate the Test Statistic:** - \(Z_{\text{STAT}} = 1.14\) (Calculated as needed. Rounded to two decimal places.) 3. **Calculate the p-value:** - The p-value is \(0.127\). (Rounded to three decimal places.) 4. **State the Conclusion of the Test:** - Do not reject the null hypothesis. There is insufficient evidence to conclude that the market share at the university is greater than the worldwide market share of 20.4%. **Part (b):** - **Task:** Suppose a sample of \(n = 400\) students at the same university (instead of \(n = 100\)) determines that 25% of the sample use the web browser. At the 0.05 level of significance, test if the market share at the university is greater than 20.4%. 1. **Calculate the Test Statistic for the Second Sample:** - \(Z_{\text{STAT}} = \_\_\_\_\_ \) (To be calculated. Rounded to two decimal places.) This example demonstrates the hypothesis testing process where a sample proportion is compared to a known population proportion.
Transcribed Image Text:**Hypothesis Testing Example** The worldwide market share for a particular web browser was 20.4% in a recent month. A sample of 100 random students at a certain university finds that 25 use this browser. We will complete parts (a) through (b) below. **Part (a):** - **Task:** Calculate the test statistic to determine if there is evidence that the market share at the university is different from 20.4%. 1. **Hypotheses:** - Null hypothesis (\(H_0\)): \(\pi = 0.204\) - Alternative hypothesis (\(H_1\)): \(\pi > 0.204\) 2. **Calculate the Test Statistic:** - \(Z_{\text{STAT}} = 1.14\) (Calculated as needed. Rounded to two decimal places.) 3. **Calculate the p-value:** - The p-value is \(0.127\). (Rounded to three decimal places.) 4. **State the Conclusion of the Test:** - Do not reject the null hypothesis. There is insufficient evidence to conclude that the market share at the university is greater than the worldwide market share of 20.4%. **Part (b):** - **Task:** Suppose a sample of \(n = 400\) students at the same university (instead of \(n = 100\)) determines that 25% of the sample use the web browser. At the 0.05 level of significance, test if the market share at the university is greater than 20.4%. 1. **Calculate the Test Statistic for the Second Sample:** - \(Z_{\text{STAT}} = \_\_\_\_\_ \) (To be calculated. Rounded to two decimal places.) This example demonstrates the hypothesis testing process where a sample proportion is compared to a known population proportion.
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