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.

A) Compute the standard deviation of the differences

B) Compute the standard deviation of the differences

C) Find the value of the t-statistic.

Days of the Week	Before	After
Monday	6	4
Tuesday	9	2
Wednesday	10	5
Thursday	4	4
Friday	7	6
Saturday	12	6
Sunday	10	8

Answer 1

SAMPLE 1	SAMPLE 2	difference , Di =sample1-sample2	(Di - Dbar)²
6	4	2.000	1.653
9	2	7.000	13.796
10	5	5.000	2.939
4	4	0.000	10.796
7	6	1.000	5.224
12	6	6.000	7.367
10	8	2.000	1.653

	sample 1	sample 2	Di	(Di - Dbar)²
sum =	58	35	23.000	43.429

mean of difference ,    D̅ =ΣDi / n =   3.286                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    2.6904                  
                          
std error of mean difference, SE = Sd / √n =    2.6904   / √   7   =   1.0169      
                          
t-statistic = (D̅ - µd)/SE = (   3.286 -   0   ) /    1.0169   =   3.2312