Given the two independent samples below, conduct a hypothesis test for the desired scenario. Assume all populations are approximately normally distributed. Sample 1 Sample 2 n1 = 861 n2 = 867 381 285 81 = 150 S2 = 180 Test the claim:

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Given the two independent samples below, conduct a hypothesis test for the desired scenario. Assume all populations are approximately normally distributed.

| Sample 1             | Sample 2             |
|----------------------|----------------------|
| \( n_1 = 861 \)      | \( n_2 = 867 \)      |
| \( \bar{x}_1 = 381 \)| \( \bar{x}_2 = 285 \)|
| \( s_1 = 150 \)      | \( s_2 = 180 \)      |

**Test the claim:**

Given the null and alternative hypotheses below, conduct a hypothesis test for \( \alpha = 0.05 \).

- \( H_0: \mu_1 = \mu_2 \)
- \( H_a: \mu_1 < \mu_2 \)

a. Given the alternative hypothesis, the test is  
   - [Select an answer]

b. Determine the test statistic. *Round to four decimal places.*  
   \( t = \) [__________]

c. Find the *p-value*. *Round to 4 decimals.*  
   \( p\text{-value} = \) [__________]

d. Make a decision.  
   - [ ] Fail to reject the null hypothesis.  
   - [ ] Reject the null hypothesis.
Transcribed Image Text:Given the two independent samples below, conduct a hypothesis test for the desired scenario. Assume all populations are approximately normally distributed. | Sample 1 | Sample 2 | |----------------------|----------------------| | \( n_1 = 861 \) | \( n_2 = 867 \) | | \( \bar{x}_1 = 381 \)| \( \bar{x}_2 = 285 \)| | \( s_1 = 150 \) | \( s_2 = 180 \) | **Test the claim:** Given the null and alternative hypotheses below, conduct a hypothesis test for \( \alpha = 0.05 \). - \( H_0: \mu_1 = \mu_2 \) - \( H_a: \mu_1 < \mu_2 \) a. Given the alternative hypothesis, the test is - [Select an answer] b. Determine the test statistic. *Round to four decimal places.* \( t = \) [__________] c. Find the *p-value*. *Round to 4 decimals.* \( p\text{-value} = \) [__________] d. Make a decision. - [ ] Fail to reject the null hypothesis. - [ ] Reject the null hypothesis.
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