Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .025 significance level. The null and alternative hypothesis would be: Ho: PM = PF Ho: PM = μF Ho: PM = HF H₁:PMPF H₁:μM PF H₁ PM PF H₁:μM > µF
Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .025 significance level. The null and alternative hypothesis would be: Ho: PM = PF Ho: PM = μF Ho: PM = HF H₁:PMPF H₁:μM PF H₁ PM PF H₁:μM > µF
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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Transcribed Image Text:**Hypothesis Testing on Cat Ownership**
**Objective:**
Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the 0.025 significance level.
**Hypotheses:**
- **Null Hypothesis (H₀):** pₘ = pₜ (The proportion of men who own cats is equal to the proportion of women.)
- **Alternative Hypothesis (H₁):** pₘ < pₜ (The proportion of men who own cats is smaller than the proportion of women.)
**Test Type:**
- One-tailed (left-tailed)
**Data Summary:**
- **Men:**
- Sample size = 80
- Proportion owning cats = 35%
- **Women:**
- Sample size = 40
- Proportion owning cats = 45%
**Statistical Analysis:**
- **Test Statistic:** Calculated value (rounded to 2 decimal places)
- **P-value:** Calculated value (rounded to 2 decimal places)
**Decision Rule:**
- **Reject the null hypothesis:** If the p-value is less than the significance level (0.025).
- **Fail to reject the null hypothesis:** If the p-value is greater than the significance level (0.025).
Choose the appropriate hypothesis and test type to perform the analysis. Calculate the test statistic and p-value accordingly, and then decide whether you can reject the null hypothesis based on the calculated p-value.
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