onsider the following hypothesis test. The following results are for two independent samples taken from the two populations. H: µ1 – 42 > 0 Sample 1 Sample 2 n = 40 50 T1 = 25.2 I2 = 22.8 a. What is the value of the test statistic (round to 2 decimals)? o1 = 5.2 Oz = 6.0 b. What is the p-value (round to 4 decimals)? Use z-value rounded to 2 decimal places.

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The image presents a hypothesis testing scenario for two independent samples from two populations. 

### Hypothesis Test
The hypotheses being tested are:
- Null Hypothesis (\( H_0 \)): \( \mu_1 - \mu_2 \leq 0 \)
- Alternative Hypothesis (\( H_a \)): \( \mu_1 - \mu_2 > 0 \)

### Sample Data
The following results are provided for the two samples:

- **Sample 1:**
  - Sample size (\( n_1 \)) = 40
  - Sample mean (\( \bar{x}_1 \)) = 25.2
  - Standard deviation (\( \sigma_1 \)) = 5.2

- **Sample 2:**
  - Sample size (\( n_2 \)) = 50
  - Sample mean (\( \bar{x}_2 \)) = 22.8
  - Standard deviation (\( \sigma_2 \)) = 6.0

### Questions

a. **Test Statistic Calculation:**
   - Find the value of the test statistic, and round it to 2 decimal places.

b. **P-value Calculation:**
   - Calculate the p-value using the z-value, and round to 4 decimal places.

c. **Hypothesis Testing Conclusion:**
   - With a significance level (\( \alpha \)) of 0.05, determine the conclusion of the hypothesis test. Choose the correct option to support the null hypothesis (\( H_0 \)) or not.

**Icon Key:** Not provided in the image.

This setup assists in analyzing the difference in means between two populations using statistical hypothesis testing techniques.
Transcribed Image Text:The image presents a hypothesis testing scenario for two independent samples from two populations. ### Hypothesis Test The hypotheses being tested are: - Null Hypothesis (\( H_0 \)): \( \mu_1 - \mu_2 \leq 0 \) - Alternative Hypothesis (\( H_a \)): \( \mu_1 - \mu_2 > 0 \) ### Sample Data The following results are provided for the two samples: - **Sample 1:** - Sample size (\( n_1 \)) = 40 - Sample mean (\( \bar{x}_1 \)) = 25.2 - Standard deviation (\( \sigma_1 \)) = 5.2 - **Sample 2:** - Sample size (\( n_2 \)) = 50 - Sample mean (\( \bar{x}_2 \)) = 22.8 - Standard deviation (\( \sigma_2 \)) = 6.0 ### Questions a. **Test Statistic Calculation:** - Find the value of the test statistic, and round it to 2 decimal places. b. **P-value Calculation:** - Calculate the p-value using the z-value, and round to 4 decimal places. c. **Hypothesis Testing Conclusion:** - With a significance level (\( \alpha \)) of 0.05, determine the conclusion of the hypothesis test. Choose the correct option to support the null hypothesis (\( H_0 \)) or not. **Icon Key:** Not provided in the image. This setup assists in analyzing the difference in means between two populations using statistical hypothesis testing techniques.
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