b. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean. (Round to three decimal places as needed.)

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Chapter1: Starting With Matlab
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A study was conducted involving a treatment group and a placebo group. The results are summarized in the table, which assumes that the two samples are independent simple random samples drawn from normally distributed populations. The population standard deviations are considered equal. A 0.05 significance level is set for both parts.

### Table Summary
|            | Treatment (\(H_1\)) | Placebo (\(H_2\)) |
|------------|---------------------|--------------------|
| Sample Size (\(n\))    | 26                  | 34                  |
| Mean (\(x\))           | 2.32                | 2.66                |
| Standard Deviation (\(s\)) | 0.61                | 0.99                |

### Hypotheses Options:
1. **Option A:** 
   - Null Hypothesis (\(H_0\)): \( \mu_1 = \mu_2 \)
   - Alternative Hypothesis (\(H_1\)): \( \mu_1 < \mu_2 \)

2. **Option B:** 
   - Null Hypothesis (\(H_0\)): \( \mu_1 = \mu_2 \)
   - Alternative Hypothesis (\(H_1\)): \( \mu_1 > \mu_2 \)

3. **Option C:** 
   - Null Hypothesis (\(H_0\)): \( \mu_1 = \mu_2 \)
   - Alternative Hypothesis (\(H_1\)): \( \mu_1 \neq \mu_2 \)

4. **Option D:** 
   - Null Hypothesis (\(H_0\)): \( \mu_1 = \mu_2 \)
   - Alternative Hypothesis (\(H_1\)): \( \mu_1 > \mu_2 \)

### Test Results:
- **Test Statistic (\(t\)):** \(-1.64\) (rounded to two decimal places).
- **P-value:** \(0.107\) (rounded to three decimal places).

### Conclusion for the Test:
- Option C is selected: Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

### Part b:
Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.

\[ (\mu_1
Transcribed Image Text:A study was conducted involving a treatment group and a placebo group. The results are summarized in the table, which assumes that the two samples are independent simple random samples drawn from normally distributed populations. The population standard deviations are considered equal. A 0.05 significance level is set for both parts. ### Table Summary | | Treatment (\(H_1\)) | Placebo (\(H_2\)) | |------------|---------------------|--------------------| | Sample Size (\(n\)) | 26 | 34 | | Mean (\(x\)) | 2.32 | 2.66 | | Standard Deviation (\(s\)) | 0.61 | 0.99 | ### Hypotheses Options: 1. **Option A:** - Null Hypothesis (\(H_0\)): \( \mu_1 = \mu_2 \) - Alternative Hypothesis (\(H_1\)): \( \mu_1 < \mu_2 \) 2. **Option B:** - Null Hypothesis (\(H_0\)): \( \mu_1 = \mu_2 \) - Alternative Hypothesis (\(H_1\)): \( \mu_1 > \mu_2 \) 3. **Option C:** - Null Hypothesis (\(H_0\)): \( \mu_1 = \mu_2 \) - Alternative Hypothesis (\(H_1\)): \( \mu_1 \neq \mu_2 \) 4. **Option D:** - Null Hypothesis (\(H_0\)): \( \mu_1 = \mu_2 \) - Alternative Hypothesis (\(H_1\)): \( \mu_1 > \mu_2 \) ### Test Results: - **Test Statistic (\(t\)):** \(-1.64\) (rounded to two decimal places). - **P-value:** \(0.107\) (rounded to three decimal places). ### Conclusion for the Test: - Option C is selected: Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. ### Part b: Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean. \[ (\mu_1
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