1. Use the sample data below to test the hypotheses Ho: P1 = P2 P3 H: Not all population proportions are equal where p; is the population proportion of Yes responses for population i. Using a .05 level of significance, what is the p-value and what is your conclusion? Populations Response 1 Yes 150 150 96 100 150 104 No

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**Hypothesis Testing Example**

1. **Objective:** Use the sample data below to test the hypotheses:

   - Null Hypothesis (\(H_0\)): \(p_1 = p_2 = p_3\)
   - Alternative Hypothesis (\(H_a\)): Not all population proportions are equal

   Where \(p_i\) is the population proportion of Yes responses for population \(i\). Using a 0.05 level of significance, what is the p-value and what is your conclusion?

**Data Table:**

- **Response:**
  - **Yes**
    - Population 1: 150
    - Population 2: 150
    - Population 3: 96
  - **No**
    - Population 1: 100
    - Population 2: 150
    - Population 3: 104

**Instructions:**

To analyze the data, apply a statistical test appropriate for comparing proportions, such as the Chi-Square Test for Homogeneity. Calculate the p-value and compare it with the significance level of 0.05 to determine whether to reject the null hypothesis. Conclude whether there is a significant difference in the population proportions.
Transcribed Image Text:**Hypothesis Testing Example** 1. **Objective:** Use the sample data below to test the hypotheses: - Null Hypothesis (\(H_0\)): \(p_1 = p_2 = p_3\) - Alternative Hypothesis (\(H_a\)): Not all population proportions are equal Where \(p_i\) is the population proportion of Yes responses for population \(i\). Using a 0.05 level of significance, what is the p-value and what is your conclusion? **Data Table:** - **Response:** - **Yes** - Population 1: 150 - Population 2: 150 - Population 3: 96 - **No** - Population 1: 100 - Population 2: 150 - Population 3: 104 **Instructions:** To analyze the data, apply a statistical test appropriate for comparing proportions, such as the Chi-Square Test for Homogeneity. Calculate the p-value and compare it with the significance level of 0.05 to determine whether to reject the null hypothesis. Conclude whether there is a significant difference in the population proportions.
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