Chapter 12: Q. 12.26 (page 492)

Road Rage. The report Controlling Road Rage: A Literature Review and Pilot Study was prepared for the AAA Foundation for Traffic Safety by D. Rathbone and. 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 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?

Short Answer

Expert verified

Ans: we reject the null hypothesis. Therefore, there is enough evidence to support the claim that road-rage incidents are more likely to occur on some days than on others.

Step by step solution

Step 1. Given information.

given,

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

Step 2. It is said that incidents of street violence are more likely to occur on some days than others. Below the claim are some common misconceptions:

Step 1-

$H_{0}$ : Road accidents are likely to occur someday.

$H_{1}$ : Road accidents are more common on some days than on others.

Step 2-

We performed the test at a $5 %$ significance level, so $α = 0.05$

Step 3-

To test the null hypothesis we have the test statistics as follows,
$χ^{2} = \sum \frac{(O - E)^{2}}{E}$

Where $O$ is the observed and $E$ is to expected frequencies.

For the expected (E) frequencies we have,

$\begin{aligned} E = n p \\ p = \frac{1}{7} (number of days 7) \\ n = \sum O = 69 \end{aligned}$

So, the expected frequency for each observed frequency is $9.86$ .

Step 3. By using the above values test statistics value are as follows,

O	E	${(O - E)}^{2}$	$\frac{{(O - E)}^{2}}{E}$
5	9.86	23.6196	2.3955
5	9.86	23.6196	2.3955
11	9.86	1.2996	0.13181
12	9.86	4.5796	0.46446
11	9.86	1.2996	0.13181
18	9.86	66.2596	6.72004
7	9.86	8.1796	0.82957
			13.0687

$\begin{aligned} χ^{2} = \sum \frac{(O - E)^{2}}{E} \\ = 13.069 \end{aligned}$

Step 4.

Step 5. Now,

Step 5:

The calculated test statistic value $x^{2} = 13.069$ is greater than the critical value ${x^{2}}_{0.05} = 12.592$ ,

so we reject the null hypothesis. Therefore, there is enough evidence to support the claim that road-rage incidents are more likely to occur on some days than on others.