9.2.12-T Question Help ▼ Independent random samples selected from two normal populations produced the sample means and standard deviations shown to the right. a. Assuming equal variances, conduct the test Ho: (H1 - H2) =0 against H: (H1 -H2) *0 using a = 0.05. b. Find and interpret the 95% confidence interval for (H -H2)- Sample 1 Sample 2 n; = 17 n2 = 14 x, = 5.9 x2 =7.9 s, =3.7 s=4.4 a. Find the test statistic. The test statistic is. (Round to two decimal places as needed.)

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### Hypothesis Testing and Confidence Interval Calculation

#### Problem Statement:

Independent random samples selected from two normal populations produced the sample means and standard deviations shown to the right.

1. **Test the Hypothesis**:
   - Assuming equal variances, conduct the test \( H_0: (\mu_1 - \mu_2) = 0 \) against \( H_1: (\mu_1 - \mu_2) \neq 0 \) using \( \alpha = 0.05 \).

2. **Calculate Confidence Interval**:
   - Find and interpret the 95% confidence interval for \( (\mu_1 - \mu_2) \).

#### Data Provided:

The following table shows the sample sizes (n), sample means (\(\bar{x}\)), and sample standard deviations (s):

|    | Sample 1 | Sample 2 |
|----|----------|----------|
| n  | 17       | 14       |
| \(\bar{x}\)  | 5.9      | 7.9      |
| s  | 3.7      | 4.4      |

#### Tasks:

**1. Find the Test Statistic:**

   a. The test statistic is \[ [ \square ] \]
      (Round to two decimal places as needed.)

**2. Calculate and Interpret the 95% Confidence Interval for \( (\mu_1 - \mu_2) \):**

   b. [Provide the interpretation here]

By solving the above tasks, you'll be able to assess the hypothesis and interpret the confidence interval, thus gaining insights from the given samples. Consider using the appropriate statistical formulas for hypothesis testing and confidence interval calculations.

---

Note: For detailed graphical explanations, any significant diagrams or charts would be described explicitly. However, the text does not provide any.
Transcribed Image Text:### Hypothesis Testing and Confidence Interval Calculation #### Problem Statement: Independent random samples selected from two normal populations produced the sample means and standard deviations shown to the right. 1. **Test the Hypothesis**: - Assuming equal variances, conduct the test \( H_0: (\mu_1 - \mu_2) = 0 \) against \( H_1: (\mu_1 - \mu_2) \neq 0 \) using \( \alpha = 0.05 \). 2. **Calculate Confidence Interval**: - Find and interpret the 95% confidence interval for \( (\mu_1 - \mu_2) \). #### Data Provided: The following table shows the sample sizes (n), sample means (\(\bar{x}\)), and sample standard deviations (s): | | Sample 1 | Sample 2 | |----|----------|----------| | n | 17 | 14 | | \(\bar{x}\) | 5.9 | 7.9 | | s | 3.7 | 4.4 | #### Tasks: **1. Find the Test Statistic:** a. The test statistic is \[ [ \square ] \] (Round to two decimal places as needed.) **2. Calculate and Interpret the 95% Confidence Interval for \( (\mu_1 - \mu_2) \):** b. [Provide the interpretation here] By solving the above tasks, you'll be able to assess the hypothesis and interpret the confidence interval, thus gaining insights from the given samples. Consider using the appropriate statistical formulas for hypothesis testing and confidence interval calculations. --- Note: For detailed graphical explanations, any significant diagrams or charts would be described explicitly. However, the text does not provide any.
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