A random sample of 250 patients was selected and their workout timing and diabetes status were recorded. The following table shows the workout timing and severity of diabetes:
| Workout (in minutes) | Severity of diabetes status | ||
| Low | Moderate | High | |
| 0 −15 | 06 | 27 | 19 |
| 15 to 30 | 08 | 38 | 17 |
| 30 to 45 | 21 | 45 | 33 |
| ≥ 45 | 14 | 18 | 06 |
Test at 5% level of significance whether workout habit and diabetes are associated with to each other or not.
To test whether workout habits and diabetes severity are associated, we perform a Chi-square test for independence. Here are the steps:
1. Hypotheses
- Null Hypothesis (H0H_0): Workout timing and severity of diabetes are independent (not associated).
- Alternative Hypothesis (HaH_a): Workout timing and severity of diabetes are associated.
2. Observed Frequencies (OijO_{ij})
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