Question

The report Controlling Road Rage: A Literature Review and Pilot Study was prepared for the AAA Foundation for Traffic Safety by D. Rathbone and J. Huckabee. The authors discussed the results of a literature review and pilot study on how to prevent aggressive driving and road rage. Road rage is defined as “… an incident in which an angry or impatient motorist or passenger intentionally injures or kills another motorist, passenger, or pedestrian, or attempts or threatens to injure or kill another motorist, passenger, or pedestrian.”

One aspect of the study was to investigate road rage as a function of the day of the week. The following table provides a frequency distribution for the days on which 69 road-rage incidents occurred.

Day	Frequency
Sunday	5
Monday	5
Tuesday	11
Wednesday	12
Thursday	11
Friday	18
Saturday	7

At the 5% significance level, do the data provide sufficient evidence to conclude that road-rage incidents are more likely to occur on some days than on others?

Apply the chi-square goodness-of-fit test, using either the critical-value approach or the P- value approach, to perform the required hypothesis test.

Answer 1

Here, our null hypothesis is,

H₀: road rage incidents occur equally on all day

Vs., H_a: road rage incidents are more likely to occur on some days than on others.

Total observed frequency = 69.

Expected frequency on each day = 69/7 = 9.66

The test statistic is given by,

= 2.248+2.248+0.186+0.567+0.186+7.2+0.732=13.367

df= n-1 = 7-1=6

From chi-square table, critical value at 5% los and df= 6 is, 12.592.

Since the critical value is less than the test statistic, we reject the null hypothesis.

There is sufficient evidence to support the claim that the road rage incidents are more likely to occur on some days than on others.