Consider the following hypothesis test. Ho: µ 1 - µ 2 < 0 Hạ: µ 1 - µ 2 > 0 he following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n 1 = 40 n 2 = 70 X 1 = 25.2 X 2 = 22.9 0 1 = 5.2 0 2 = 7 1. What is the value of the test statistic (round to 2 decimals)?

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### Hypothesis Testing

Consider the following hypothesis test:

- Null Hypothesis (H₀): μ₁ - μ₂ ≤ 0
- Alternative Hypothesis (Hₐ): μ₁ - μ₂ > 0

The following results are for two independent samples taken from two populations:

#### Sample 1
- \( n_1 = 40 \)
- \( \bar{x}_1 = 25.2 \)
- \( \sigma_1 = 5.2 \)

#### Sample 2
- \( n_2 = 70 \)
- \( \bar{x}_2 = 22.9 \)
- \( \sigma_2 = 7 \)

### Questions

**a.** What is the value of the test statistic (round to 2 decimals)?  
[Answer Box]

**b.** What is the p-value (round to 4 decimals)? Use the z-table. Use z-value rounded to 2 decimal places.  
[Answer Box]

**c.** With \( \alpha = .05 \), what is your hypothesis testing conclusion?  
p-value is [Drop-down Selection] \( H_0 \)
Transcribed Image Text:### Hypothesis Testing Consider the following hypothesis test: - Null Hypothesis (H₀): μ₁ - μ₂ ≤ 0 - Alternative Hypothesis (Hₐ): μ₁ - μ₂ > 0 The following results are for two independent samples taken from two populations: #### Sample 1 - \( n_1 = 40 \) - \( \bar{x}_1 = 25.2 \) - \( \sigma_1 = 5.2 \) #### Sample 2 - \( n_2 = 70 \) - \( \bar{x}_2 = 22.9 \) - \( \sigma_2 = 7 \) ### Questions **a.** What is the value of the test statistic (round to 2 decimals)? [Answer Box] **b.** What is the p-value (round to 4 decimals)? Use the z-table. Use z-value rounded to 2 decimal places. [Answer Box] **c.** With \( \alpha = .05 \), what is your hypothesis testing conclusion? p-value is [Drop-down Selection] \( H_0 \)
**Consider the following results for two independent random samples taken from two populations.**

### Sample 1
- \( n_1 = 50 \)
- \( \bar{x}_1 = 13.9 \)
- \( \sigma_1 = 2.4 \)

### Sample 2
- \( n_2 = 30 \)
- \( \bar{x}_2 = 11.2 \)
- \( \sigma_2 = 3.5 \)

**a. What is the point estimate of the difference between the two population means? (to 1 decimal)**

[Answer Box]

**b. Provide a 90% confidence interval for the difference between the two population means (to 2 decimals). Use a z-table.**

([Answer Box], [Answer Box])

**c. Provide a 95% confidence interval for the difference between the two population means (to 2 decimals). Use a z-table. If your answer is negative, enter minus (-) sign.**

([Answer Box], [Answer Box])
Transcribed Image Text:**Consider the following results for two independent random samples taken from two populations.** ### Sample 1 - \( n_1 = 50 \) - \( \bar{x}_1 = 13.9 \) - \( \sigma_1 = 2.4 \) ### Sample 2 - \( n_2 = 30 \) - \( \bar{x}_2 = 11.2 \) - \( \sigma_2 = 3.5 \) **a. What is the point estimate of the difference between the two population means? (to 1 decimal)** [Answer Box] **b. Provide a 90% confidence interval for the difference between the two population means (to 2 decimals). Use a z-table.** ([Answer Box], [Answer Box]) **c. Provide a 95% confidence interval for the difference between the two population means (to 2 decimals). Use a z-table. If your answer is negative, enter minus (-) sign.** ([Answer Box], [Answer Box])
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