Candidate T wants to determine if there is a difference in his popularity between men and women. To test the claim of this difference, he conducts a survey of voters. The sample contains 375 men and 350 women, of which 155 men and 123 of the women favor his candidacy. Do these values indicate a significant difference in popularity? Use a 0.05 significance level. What are the hypothesis statements? Ho: Hm = Hw HA: Hm Hw %3D Ho: Pm= Pw %3D HA: Pm Pw O Ho: Pm =Pul Ithi PM> Pur O Ho Pm z Dul. HA Do Pur

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## Analyzing Candidate T's Popularity Difference Between Men and Women

### Problem Statement

Candidate T wants to determine if there is a difference in his popularity between men and women. To test this claim, he conducts a survey of voters. The sample consists of 375 men and 350 women, out of which 155 men and 123 women favor his candidacy. Do these values indicate a significant difference in popularity? Use a 0.05 significance level.

### Hypothesis Statements

1. **First Option: Mean Difference Hypothesis**
   - \( H_0: \mu_m = \mu_w \)
   - \( H_A: \mu_m \neq \mu_w \)

2. **Second Option: Proportion Difference Hypothesis**
   - \( H_0: P_m = P_w \)
   - \( H_A: P_m \neq P_w \)

3. **Third Option: Proportion Comparison Hypothesis** (Selected)
   - \( H_0: P_m \ge P_w \)
   - \( H_A: P_m < P_w \)

### Explanation

- **Graphs/Diagrams**: This document includes a list of hypothesis statements regarding the proportion of men (\( P_m \)) and women (\( P_w \)) who support Candidate T. The relevant hypothesis chosen for testing is comparing the proportion of support among men and women.
  
This example illustrates the process of hypothesis testing where different hypotheses are proposed and one is selected to determine if Candidate T's popularity significantly differs between genders using specified significance levels.
Transcribed Image Text:## Analyzing Candidate T's Popularity Difference Between Men and Women ### Problem Statement Candidate T wants to determine if there is a difference in his popularity between men and women. To test this claim, he conducts a survey of voters. The sample consists of 375 men and 350 women, out of which 155 men and 123 women favor his candidacy. Do these values indicate a significant difference in popularity? Use a 0.05 significance level. ### Hypothesis Statements 1. **First Option: Mean Difference Hypothesis** - \( H_0: \mu_m = \mu_w \) - \( H_A: \mu_m \neq \mu_w \) 2. **Second Option: Proportion Difference Hypothesis** - \( H_0: P_m = P_w \) - \( H_A: P_m \neq P_w \) 3. **Third Option: Proportion Comparison Hypothesis** (Selected) - \( H_0: P_m \ge P_w \) - \( H_A: P_m < P_w \) ### Explanation - **Graphs/Diagrams**: This document includes a list of hypothesis statements regarding the proportion of men (\( P_m \)) and women (\( P_w \)) who support Candidate T. The relevant hypothesis chosen for testing is comparing the proportion of support among men and women. This example illustrates the process of hypothesis testing where different hypotheses are proposed and one is selected to determine if Candidate T's popularity significantly differs between genders using specified significance levels.
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