Final answer:
To determine if the accident profile of engineers differs from the general driving population, a Chi-square test comparing observed and expected frequencies is used. By calculating the Chi-square statistic and comparing it to the critical value, we can infer statistical significance.
Step-by-step explanation:
The question at hand requires an analysis to determine if the observed pattern of accidents among engineers is statistically significant from the pattern of the general driving population. We will use a Chi-square test to infer whether the proportions of accidents among engineers differ from those in the regional data.
Firstly, we establish the expected frequencies for our sample size of 440 engineers, based on the regional accident data:
- 82% with no accidents: 0.82 * 440 = 360.8 expected
- 15% with 1 accident: 0.15 * 440 = 66 expected
- 3% with 2 or more accidents: 0.03 * 440 = 13.2 expected
The observed frequencies from the sample are:
- 366 had no accidents
- 68 had exactly 1 accident
- 6 had 2 or more accidents
We calculate the Chi-square statistic using the formula:
Chi-square = ∑ [(observed - expected)^2 / expected]
After computing this value and comparing it to the critical value from the Chi-square distribution with the appropriate degrees of freedom and significance level, it can be determined if the deviation of the engineers' accident data from the expected values based on the general population is significant.
If the computed Chi-square statistic is greater than the critical value, we reject the null hypothesis that engineers follow the same accident profile. Conversely, if the Chi-square statistic is lower, we do not have enough evidence to suggest that the accident profile of engineers is different.