Test the claim that the proportion of people who own cats is larger than 50% at the 0.025 significance level.

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**Statistical Hypothesis Testing on Cat Ownership**

**Problem Statement:**
Test the claim that the proportion of people who own cats is larger than 50% at the 0.025 significance level.

**Hypotheses:**
The null and alternative hypotheses would be:

1. \( H_0: p = 0.5 \) (The proportion of cat owners is 50%)
   - \( H_1: p \neq 0.5 \) 
   - \( H_0: \mu \geq 0.5 \) 
   - \( H_1: \mu < 0.5 \)
   - \( H_0: p \leq 0.5 \) 
   - \( H_1: p > 0.5 \)

2. \( H_0: \mu = 0.5 \)
   - \( H_1: \mu \neq 0.5 \)
   - \( H_0: \mu \leq 0.5 \)
   - \( H_1: \mu > 0.5 \)
   - \( H_0: p \geq 0.5 \)
   - \( H_1: p < 0.5 \)

**Test Type:**
Select the appropriate test type:
- Two-tailed
- Right-tailed
- Left-tailed

**Sample Information:**
Based on a sample of 200 people, 59% owned cats.

**Instructions:**
Use this information to perform your hypothesis test, comparing the sample proportion to the hypothesized population proportion to determine if there is significant evidence to support the claim. Select the correct null and alternative hypotheses and determine the tail type based on the claim.
Transcribed Image Text:**Statistical Hypothesis Testing on Cat Ownership** **Problem Statement:** Test the claim that the proportion of people who own cats is larger than 50% at the 0.025 significance level. **Hypotheses:** The null and alternative hypotheses would be: 1. \( H_0: p = 0.5 \) (The proportion of cat owners is 50%) - \( H_1: p \neq 0.5 \) - \( H_0: \mu \geq 0.5 \) - \( H_1: \mu < 0.5 \) - \( H_0: p \leq 0.5 \) - \( H_1: p > 0.5 \) 2. \( H_0: \mu = 0.5 \) - \( H_1: \mu \neq 0.5 \) - \( H_0: \mu \leq 0.5 \) - \( H_1: \mu > 0.5 \) - \( H_0: p \geq 0.5 \) - \( H_1: p < 0.5 \) **Test Type:** Select the appropriate test type: - Two-tailed - Right-tailed - Left-tailed **Sample Information:** Based on a sample of 200 people, 59% owned cats. **Instructions:** Use this information to perform your hypothesis test, comparing the sample proportion to the hypothesized population proportion to determine if there is significant evidence to support the claim. Select the correct null and alternative hypotheses and determine the tail type based on the claim.
### Hypothesis Testing

**Test Type Selection:**
- Two-tailed
- Right-tailed
- Left-tailed

**Sample Data:**
Based on a sample of 200 people, 59% owned cats.

**P-value Calculation:**
The p-value is: [Input Box] (to 2 decimals)

**Decision Making:**
Based on this we:
- [ ] Reject the null hypothesis
- [ ] Fail to reject the null hypothesis

### Explanation:
This section is designed to help students understand and conduct hypothesis testing. Select the appropriate test type by considering the research question and hypotheses. Enter the calculated p-value, and make a decision based on the statistical significance level.
Transcribed Image Text:### Hypothesis Testing **Test Type Selection:** - Two-tailed - Right-tailed - Left-tailed **Sample Data:** Based on a sample of 200 people, 59% owned cats. **P-value Calculation:** The p-value is: [Input Box] (to 2 decimals) **Decision Making:** Based on this we: - [ ] Reject the null hypothesis - [ ] Fail to reject the null hypothesis ### Explanation: This section is designed to help students understand and conduct hypothesis testing. Select the appropriate test type by considering the research question and hypotheses. Enter the calculated p-value, and make a decision based on the statistical significance level.
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