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The test statistic leads to a decision to ... reject the null accept or fail to reject the null
![You are conducting a hypothesis test to evaluate the claim (\(H_a\)) at a significance level of \(\alpha = 0.02\).
### Hypotheses:
- Null Hypothesis (\(H_0\)): \(\mu_1 = \mu_2\)
- Alternative Hypothesis (\(H_a\)): \(\mu_1 < \mu_2\)
### Data Samples:
#### Sample #1:
- Data Points: 66.1, 66.1, 69.3, 66.6, 47.1, 91.1, 73.1, 75.7, 88.2, 67.8, 77.8, 88.2, 77.1, 85.4, 56.4, 98.5, 80.2, 92.1, 80.6, 93.2, 86.6, 74.9, 55.2, 75.6, 90.4, 89.1, 68.8, 73.1, 91.5, 78.2, 74.9, 49.9, 84.7, 93.2, 73.6, 58.6, 78.6, 68.8, 58.6, 64.2, 104, 89.6, 106.7, 76.9, 104, 86.8, 72.2, 88.6, 79.8
#### Sample #2:
- Data Points: 86.8, 98, 83.4, 89, 89.8, 96, 83.1, 74.2, 75.3, 83.1, 87.1, 94.3, 101, 86.2, 80.9, 87.3, 84.8, 94, 95.7, 80.6, 96.4, 94.6, 99.9, 77.2, 90.1, 89.2, 88.1, 73, 100.4, 84, 95, 104.5, 99.9, 86, 62.2](https://content.bartleby.com/qna-images/question/fdcdac8c-d150-4809-97f8-c65740958103/2f4e3f66-35f5-4587-99f3-54263de1e0b0/ry418q_thumbnail.jpeg)
Transcribed Image Text:You are conducting a hypothesis test to evaluate the claim (\(H_a\)) at a significance level of \(\alpha = 0.02\).
### Hypotheses:
- Null Hypothesis (\(H_0\)): \(\mu_1 = \mu_2\)
- Alternative Hypothesis (\(H_a\)): \(\mu_1 < \mu_2\)
### Data Samples:
#### Sample #1:
- Data Points: 66.1, 66.1, 69.3, 66.6, 47.1, 91.1, 73.1, 75.7, 88.2, 67.8, 77.8, 88.2, 77.1, 85.4, 56.4, 98.5, 80.2, 92.1, 80.6, 93.2, 86.6, 74.9, 55.2, 75.6, 90.4, 89.1, 68.8, 73.1, 91.5, 78.2, 74.9, 49.9, 84.7, 93.2, 73.6, 58.6, 78.6, 68.8, 58.6, 64.2, 104, 89.6, 106.7, 76.9, 104, 86.8, 72.2, 88.6, 79.8
#### Sample #2:
- Data Points: 86.8, 98, 83.4, 89, 89.8, 96, 83.1, 74.2, 75.3, 83.1, 87.1, 94.3, 101, 86.2, 80.9, 87.3, 84.8, 94, 95.7, 80.6, 96.4, 94.6, 99.9, 77.2, 90.1, 89.2, 88.1, 73, 100.4, 84, 95, 104.5, 99.9, 86, 62.2
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