Question

DRUNK DRIVING TESTING LABS

You are the owner of ABC Testing Company and have been hired by an insurance company to do research regarding drunk driving. You have purchased a driving simulator which allows a subject to take a simulated road test and then provides a score indicating the number of driver’s driving errors committed during the test drive. During the road test problems appear at random and not all problems appear in each road test. You select a random sample of 25 drivers and ask each one to take the test drive on the simulator. The number of errors for each driver is recorded. Next you ask each of the individuals in the group to drink three 16-ounce cans of beer in a 60-minute period and take another simulated driving test.

The results are shown in the table below.

The research question is: Does alcohol impair the driver’s ability and therefore increase the number of driving errors?

You believe the distribution of scores on the test drive does not follow a normal distribution and so a nonparametric test should be used. Because the observations are paired you decide to use both the sign test and the Wilcoxon signed-rank test. You will:

1. Create an Excel file using the data given above.
2. Compare the results using these two procedures. Conduct an appropriate test of hypotheses to determine if alcohol is related to driving errors.
3. Write a report to the insurance company detailing your methodology, showing your calculations and comparisons between the two methods used, and summarize your findings using charts, tables, graphs.

Answer 1

Solution:

The Pie chart for Without Alcohol is:

The Pie chart for With Alcohol is:

The histogram of Without Alcohol is:

The data is not normally distributed from the histogram for Without Alcohol.

The histogram of With Alcohol is:

The data is not normally distributed from the histogram for With Alcohol.

Let us conduct a Paired t-test as the Parametric Test.

The hypothesis being tested is:

H₀: µ₁ = µ₂

H₁: µ₁ ≠ µ₂

The output is:

81.200	mean Without Alcohol
88.320	mean With Alcohol
-7.120	mean difference (Without Alcohol - With Alcohol)
12.508	std. dev.
2.502	std. error
25	n
24	df
-2.846	t
.0089	p-value (two-tailed)

Since the p-value (0.0089) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that Alcohol is related to driving errors.

Let us conduct a Wilcoxon Signed-Rank Test as the Non-Parametric Test.

The hypothesis being tested is:

H₀: The median difference, M, is equal to zero.

H₁: The median difference, M, is not equal to zero.

The output is:

	variables:	Without Alcohol - With Alcohol
	70.5	sum of positive ranks
	229.5	sum of negative ranks
	24	n
	150.000	expected value
	35.000	standard deviation
	-2.271	z
	.0231	p-value (two-tailed)
No.	Data	Rank
1	-14	17
2	-5	7
3	9	11.5
4	10	14
5	1	1.5
6	2	4.5
7	-20	19.5
8	-25	22
9	2	4.5
10	-6	8.5
11	-10	14
12	-8	10
13	-23	21
14	-34	24
15	-6	8.5
16	10	14
17	-2	4.5
18	-20	19.5
19	-15	18
20	2	4.5
21	11	16
22	-27	23
23	-1	1.5
24	-9	11.5

Since the p-value (0.0231) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that Alcohol is related to driving errors.

Therefore, the result is the same for the Parametric and Non-Parametric test.

Thus, we have enough evidence to conclude that Alcohol is related to driving errors.

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   Thank you.