Test the claim that the proportion of men who own cats is smaller than the proportion of women who ow cats at the .10 significance level. The null and alternative hypothesis would be: Ho: HM = HF Họ:µM µf Ho:PM = PF Ho:PM PF Ho: HM µF Ho:PM PF H1: µM + µF H1: µM < µF H1:PM + PF H1:PM > PF H1:µM > µF H1:PM < PF The test is: left-tailed right-tailed two-tailed Based on a sample of 60 men, 35% owned cats Based on a sample of 40 women, 55% owned cats The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals) Based on this we: O Fail to reject the null hypothesis O Reject the null hypothesis

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### Hypothesis Testing: Proportion of Cat Owners

**Objective:**
Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the 0.10 significance level.

**Hypotheses:**
- Null Hypothesis (H₀): \( p_M = p_F \)
- Alternative Hypothesis (H₁): \( p_M < p_F \)

**Question Choices for Null and Alternative Hypotheses:**
- \( H₀: \mu_M = \mu_F \)
- \( H₀: \mu_M \ne \mu_F \)
- \( H₀: \mu_M < \mu_F \)
- \( H₀: p_M = p_F \)  (correct)
- \( H₀: p_M \ne p_F \)
- \( H₀: p_M > p_F \)
- \( H₀: p_M < p_F \)  (correct)


**Test Types:**
- Left-tailed 
- Right-tailed 
- Two-tailed 
   
Answer: Left-tailed

**Sample Data:**
- **Men:** 
  - \( n_M = 60 \)
  - \( \hat{p}_M = 0.35 \) (35% owned cats)
- **Women:**
  - \( n_F = 40 \)
  - \( \hat{p}_F = 0.55 \) (55% owned cats)
  
**Calculations:**
1. **Test Statistic Calculation:**
   - The test statistic should be entered here after calculation (to 2 decimal places).

2. **p-value Calculation:**
   - The p-value should be entered here after calculation (to 2 decimal places).

**Decision Rule:**
- Determine whether to reject or fail to reject the null hypothesis based on the p-value and the significance level.

**Conclusion Based on Test:**
- Choose one of the following based on the comparison of the p-value with the significance level:
  - Fail to reject the null hypothesis
  - Reject the null hypothesis

### Summary
By completing the above steps and calculations, you will determine whether the sample data provides enough evidence to support the claim that a smaller proportion of men own cats compared to women at the 0.10 significance level.
Transcribed Image Text:### Hypothesis Testing: Proportion of Cat Owners **Objective:** Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the 0.10 significance level. **Hypotheses:** - Null Hypothesis (H₀): \( p_M = p_F \) - Alternative Hypothesis (H₁): \( p_M < p_F \) **Question Choices for Null and Alternative Hypotheses:** - \( H₀: \mu_M = \mu_F \) - \( H₀: \mu_M \ne \mu_F \) - \( H₀: \mu_M < \mu_F \) - \( H₀: p_M = p_F \) (correct) - \( H₀: p_M \ne p_F \) - \( H₀: p_M > p_F \) - \( H₀: p_M < p_F \) (correct) **Test Types:** - Left-tailed - Right-tailed - Two-tailed Answer: Left-tailed **Sample Data:** - **Men:** - \( n_M = 60 \) - \( \hat{p}_M = 0.35 \) (35% owned cats) - **Women:** - \( n_F = 40 \) - \( \hat{p}_F = 0.55 \) (55% owned cats) **Calculations:** 1. **Test Statistic Calculation:** - The test statistic should be entered here after calculation (to 2 decimal places). 2. **p-value Calculation:** - The p-value should be entered here after calculation (to 2 decimal places). **Decision Rule:** - Determine whether to reject or fail to reject the null hypothesis based on the p-value and the significance level. **Conclusion Based on Test:** - Choose one of the following based on the comparison of the p-value with the significance level: - Fail to reject the null hypothesis - Reject the null hypothesis ### Summary By completing the above steps and calculations, you will determine whether the sample data provides enough evidence to support the claim that a smaller proportion of men own cats compared to women at the 0.10 significance level.
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