You wish to test the following claim (Ha) at a significance level of a = 0.02. H₂:1 = 42 H₂:1<42 You obtain the following two samples of data. Sample #1 66.1 66.1 69.3 66.6 47.1 91.1 73.1 75.7 88.2 67.8 77.8 88.2 72.7 75.7 66.6 56.4 80.6 74.4 80.2 92.1 56.4 86 78.6 58.6 102.8 74.9 55.2 84.7 68.3 73.1 68.8 78.2 79.4 65.5 89.6 66.6 52 94.9 85.1 82.2 98.3 105.2 57.6 96.2 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 Sample #2 86.8 98 83.4 89.8 96 83.1 75.3 83.1 87.1 101 86.2 80.9 84.8 94 95.7 94 96.4 99.9 90.1 89.2 88.1 100.4 84 95 99.9 86 62.2 89 74.2 94.3 87.3 80.6 77.2 73 104.5 79.5

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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
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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