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The number of automobile accidents per week that took place during peak traffic hours in ma metropolitan city reported for 10 weeks was 12, 8, 20, 2, 14, 10, 15, 6, 9 and 4. Are the frequencies in agreement with the belief that accident conditions were the same during 10 weeks period?
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Introduction
The number of automobile accidents per week during peak traffic hours in a metropolitan city reported for 10 weeks was observed. The frequencies are to be analyzed to determine if the accident conditions were the same during the entire 10 weeks period.
Data Analysis
The following are the frequencies of automobile accidents per week during peak traffic hours for 10 weeks:
- Week 1: 12
- Week 2: 8
- Week 3: 20
- Week 4: 2
- Week 5: 14
- Week 6: 10
- Week 7: 15
- Week 8: 6
- Week 9: 9
- Week 10: 4
The following statistical measures can be computed from the data:
- Mean: 10.0
- Median: 9.5
- Mode: None
- Range: 18
- Variance: 33.2
- Standard Deviation: 5.8
Testing for Agreement
A chi-square test can be conducted to determine if the frequencies are in agreement with the belief that accident conditions were the same during the 10-week period. The null hypothesis is that the frequencies are the same, while the alternative hypothesis is that they are not.
The chi-square statistic is calculated as follows:
χ² = ∑(O - E)² / E
Where O is the observed frequency and E is the expected frequency.
The expected frequency can be calculated as the sum of all frequencies divided by the number of weeks:
E = (12 + 8 + 20 + 2 + 14 + 10 + 15 + 6 + 9 + 4) / 10 = 10
The observed and expected frequencies are:
| Week | Observed Frequency | Expected Frequency | (O - E)² / E |
|---|---|---|---|
| 1 | 12 | 10 | 0.4 |
| 2 | 8 | 10 | 0.4 |
| 3 | 20 | 10 | 10.0 |
| 4 | 2 |
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The number of automobile accidents per week that took place during peak traffic hours in ma metropolitan city reported for 10 weeks was 12, 8, 20, 2, 14, 10, 15, 6, 9 and 4. Are the frequencies in agreement with the belief that accident conditions were the same during 10 weeks period?
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