A local organization conducted a traffic study to determine if traffic collisions were more likely on Friday

Question:

A local organization conducted a traffic study to determine if traffic collisions were more likely on Friday and Saturday nights than on other nights. The city council was considering a proposal that bars in a specific district be closed earlier in an effort to reduce late- night accidents in the area. The assumption was that a larger number of traffic accidents would correspond to the heaviest bar traffic (which occurred on the weekends). Table 6.13 shows data collected on traffic accidents that had occurred in that district over the past two years.
Table 6.13 Results from the collision study.

a. Conduct a chi- square test to determine if the proportion of accidents is the same each day of the week. Write the null and alternative hypotheses and clearly state your conclusions. Do we have evidence to show that weekends are more likely to have accidents than other days?
b. Which day contributes most to the chi-square statistic? In other words, of the seven days, which day has the largest (observed €“ expected) 2/ expected value? Taking the square root of this value has some similarities to calculating standardized residuals.
c. Another way to conduct the study would be to start with the null hypothesis that weekends are twice as likely to have accidents as weekdays. Thus, the null hypothesis states that 1/ 9 of the accidents occur on each weekday, 2/ 9 of the accidents occur on Friday, and 2/ 9 of the accidents occur on Saturday. Conduct a chi-square test and clearly state your conclusions. Do we have evidence to show that weekends are more likely to have accidents than other days?
There are limitations to what can be concluded from a chi-square test. Failing to reject the null hypothesis is not the same as proving the null hypothesis is true. While we can prove that the probability of an accident in the district is not the same for each day, we can€™t state which days are more likely to have accidents. Similarly, we can prove Ha: weekends are not twice as likely to have accidents as weekdays, but failing to reject H0 does not prove that weekends are twice as likely to have accidents as weekdays.