Two different simple random samples are drawn from two different populations. The first sample consists of 40 people with 20 having a common attribute. The second sample consists of 2200 people with 1573 of them having the same common attribute. Compare the results from a hypothesis test of p₁ =P2 (with a 0.05 significance level) and a 95% confidence interval estimate of P1-P2- What are the null and alternative hypotheses for the hypothesis test? OA. Ho: P12P2 H₁: P₁ #P₂ OD. Ho: P1 P2 H₁: P₁ P2 OB. Ho: P₁ H₁: P₁ P2 P2 OE. Ho: P₁ SP₂ H₁: P1 P2 GEZER OC. Ho: P1 P2 H₁: P₁ P2 OF. Ho: P1 H₁: P₁ P2 P2

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### Hypothesis Testing Example

Two different simple random samples are drawn from two different populations. 

- **First sample**: Consists of 40 people, with 20 having a common attribute.
- **Second sample**: Consists of 2200 people, with 1573 of them having the same common attribute.

**Task**: Compare the results from a hypothesis test of \( p_1 = p_2 \) (with a 0.05 significance level) and a 95% confidence interval estimate of \( p_1 - p_2 \).

**Question**: What are the null and alternative hypotheses for the hypothesis test?

### Options

A. 
- \( H_0: p_1 \leq p_2 \)
- \( H_1: p_1 > p_2 \)

B. 
- \( H_0: p_1 \geq p_2 \)
- \( H_1: p_1 < p_2 \)

C. 
- \( H_0: p_1 \ne p_2 \)
- \( H_1: p_1 = p_2 \)

D. 
- \( H_0: p_1 = p_2 \)
- \( H_1: p_1 \ne p_2 \)

E. 
- \( H_0: p_1 \geq p_2 \)
- \( H_1: p_1 = p_2 \)

F. 
- \( H_0: p_1 = p_2 \)
- \( H_1: p_1 > p_2 \)

Select the correct hypotheses for the test, keeping in mind that the null hypothesis typically states that there is no effect or no difference.
Transcribed Image Text:### Hypothesis Testing Example Two different simple random samples are drawn from two different populations. - **First sample**: Consists of 40 people, with 20 having a common attribute. - **Second sample**: Consists of 2200 people, with 1573 of them having the same common attribute. **Task**: Compare the results from a hypothesis test of \( p_1 = p_2 \) (with a 0.05 significance level) and a 95% confidence interval estimate of \( p_1 - p_2 \). **Question**: What are the null and alternative hypotheses for the hypothesis test? ### Options A. - \( H_0: p_1 \leq p_2 \) - \( H_1: p_1 > p_2 \) B. - \( H_0: p_1 \geq p_2 \) - \( H_1: p_1 < p_2 \) C. - \( H_0: p_1 \ne p_2 \) - \( H_1: p_1 = p_2 \) D. - \( H_0: p_1 = p_2 \) - \( H_1: p_1 \ne p_2 \) E. - \( H_0: p_1 \geq p_2 \) - \( H_1: p_1 = p_2 \) F. - \( H_0: p_1 = p_2 \) - \( H_1: p_1 > p_2 \) Select the correct hypotheses for the test, keeping in mind that the null hypothesis typically states that there is no effect or no difference.
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