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d. The p-value = 0.4238 x (Please show your answer to 4 decimal places.) e. The p-value is sa f. Based on this, we should reject a Thus the final conclusion is that the null hypothesis.

d. The p-value = 0.4238 x (Please show your answer to 4 decimal places.) e. The p-value is sa f. Based on this, we should reject a Thus the final conclusion is that the null hypothesis.

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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Need help find the P-value.
### Statistical Analysis of College Graduation Rates **Problem Statement:** - **Objective:** Determine if the percentage of students who play intramural sports and receive a degree within six years is significantly larger than the general 56% of students at four-year colleges who receive a degree within the same time frame. - **Data:** Of the 278 students who played intramural sports, 170 received a degree within six years. - **Significance Level:** α = 0.10. **Steps and Calculations:** a. **Statistical Method:** - For this study, we use a **z-test for a population proportion**. b. **Hypotheses:** - **Null Hypothesis (H0):** p = 0.56 - **Alternative Hypothesis (H1):** p > 0.56 c. **Test Statistic:** - The calculated z-test statistic is **1.730**. d. **Significance Testing:** - **p-value:** 0.4238 e. **Comparison to Significance Level:** - p-value (0.4238) is compared against α = 0.10. f. **Decision:** - Since the p-value is **greater than** α, we **do not reject** the null hypothesis. g. **Conclusion:** - There is **not sufficient evidence** to conclude that the population proportion of students who played intramural sports and graduated is significantly larger than 56% at the 0.10 significance level. ### Explanation of Processes: 1. **Z-Test for a Population Proportion:** - A z-test is employed to compare the observed proportion to a theoretical one when the sample size is large. 2. **Hypotheses Setup:** - Null hypothesis suggests no increase in graduation rates among intramural sports participants, while the alternative proposes a significant increase. 3. **Calculating the Test Statistic:** - A z-score is calculated to standardize the observed outcome under the assumption that the null hypothesis is true. 4. **P-Value Interpretation:** - The p-value indicates the probability of observing a test statistic as extreme as, or more extreme than, the observed, under the null hypothesis. By understanding these steps, students can analyze data and assess hypotheses regarding population proportions in various contexts.
Transcribed Image Text:### Statistical Analysis of College Graduation Rates **Problem Statement:** - **Objective:** Determine if the percentage of students who play intramural sports and receive a degree within six years is significantly larger than the general 56% of students at four-year colleges who receive a degree within the same time frame. - **Data:** Of the 278 students who played intramural sports, 170 received a degree within six years. - **Significance Level:** α = 0.10. **Steps and Calculations:** a. **Statistical Method:** - For this study, we use a **z-test for a population proportion**. b. **Hypotheses:** - **Null Hypothesis (H0):** p = 0.56 - **Alternative Hypothesis (H1):** p > 0.56 c. **Test Statistic:** - The calculated z-test statistic is **1.730**. d. **Significance Testing:** - **p-value:** 0.4238 e. **Comparison to Significance Level:** - p-value (0.4238) is compared against α = 0.10. f. **Decision:** - Since the p-value is **greater than** α, we **do not reject** the null hypothesis. g. **Conclusion:** - There is **not sufficient evidence** to conclude that the population proportion of students who played intramural sports and graduated is significantly larger than 56% at the 0.10 significance level. ### Explanation of Processes: 1. **Z-Test for a Population Proportion:** - A z-test is employed to compare the observed proportion to a theoretical one when the sample size is large. 2. **Hypotheses Setup:** - Null hypothesis suggests no increase in graduation rates among intramural sports participants, while the alternative proposes a significant increase. 3. **Calculating the Test Statistic:** - A z-score is calculated to standardize the observed outcome under the assumption that the null hypothesis is true. 4. **P-Value Interpretation:** - The p-value indicates the probability of observing a test statistic as extreme as, or more extreme than, the observed, under the null hypothesis. By understanding these steps, students can analyze data and assess hypotheses regarding population proportions in various contexts.
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