Question

A city wants to know if a new advertising campaign to make citizens aware of the dangers of driving after drinking has been effective. The accompanying table shows the number of drivers who have been stopped with more alcohol in their systems than the law allows for each day of the week in the week before and the week a month after the campaign starts. Assume that the data from each population is Normally distributed. Complete parts a through i below.

Day of the Week	Before			After
M	4			1
T	3			4
W	4			3
Th	8			3
F	3			5
S	11			10
Su	7			8

​a) Are the data​ paired? Explain. Choose the correct answer below.

A.​Yes, because each day of the week was compared before and after the advertisement.

B.​Yes, because the before counts were compared to the counts after the advertisement.

C. ​No, they are not paired because the drivers are independent of each other.

​b) Compute the mean difference. Find the mean difference of ​(before−​after).

​c) Compute the standard deviation of the differences.

​d) Compute the standard error of the mean difference.

​e) Find the value of the​ t-statistic.

​f) How many degrees of freedom does the​ t-statistic have?

​g) Is the alternative​ one- or​ two-sided? Explain.

Choose the correct answer below.

A. It is​ two-sided, because the city wants want to know if the advertisement changed the number of drunk drivers.

B. It is​ one-sided, because the city wants to know if the advertisement changed the number of drunk drivers.

C. It is​ one-sided, because the city wants to know if the advertisement lowers the number of drunk drivers.

D. It is​ two-sided, because the city wants to know if the advertisement lowers the number of drunk drivers.

h) What is the​ P-value associated with this​ t-statistic? Assume that the other assumptions and conditions for inference are met.

i) At α=0.10​, what do you​ conclude?

(REJECT OR DO NOT REJECT) H0 . There (IS OR IS NOT) sufficient evidence to conclude that the advertising lowered the mean number of drunk drivers on the road.

Answer 1

Ans a)

A.​Yes, because each day of the week was compared before and after the advertisement

using minitab>stta>basci stat>paired t

we have

Paired T-Test and CI: Before, After

Paired T for Before - After

N Mean StDev SE Mean
Before 7 5.71 3.04 1.15
After 7 4.86 3.13 1.18
Difference 7 0.857 2.478 0.937

95% CI for mean difference: (-1.435, 3.149)
T-Test of mean difference = 0 (vs ≠ 0): T-Value = 0.91 P-Value = 0.395

​b) the mean difference is 0.857

​c) the standard deviation of the differences is 2.478

​d) the standard error of the mean difference is 0.802

​e) the value of the​ t-statistic is 0.91

​f) degree of freedom is 6

​g) the alternative​ is one sided

C. It is​ one-sided, because the city wants to know if the advertisement lowers the number of drunk drivers

h) s the​ P-value associated with this​ t-statistic is 0.395

i) since p value >0.10

DO NOT REJECT H0 . There IS NOT sufficient evidence to conclude that the advertising lowered the mean number of drunk drivers on the road.