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	10	1
T	3	1
W	9	5
Th	5	4
F	3	9
S	18	7
Su	5	8

a) Are the data​ paired? Explain.

Choose the correct answer below.

A.

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

B.

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

advertisement.

C.

​Yes, because the before counts were compared to the counts after the

advertisement.

​b) Compute the mean difference.

Find the mean difference of

​(beforeminus

​after).

d overbar

equalsnothing

drivers

​(Round to three decimal places as​ needed.)

​c) Compute the standard deviation of the differences.

s Subscript d

equalsnothing

​(Round to three decimal places as​ needed.)

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

SE left parenthesis d overbar right parenthesis

equalsnothing

​(Round to three decimal places as​ needed.)

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

tequals

nothing

​(Round to three decimal places as​ needed.)

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

dfequals

nothing

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

D.

It is​ one-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.

​P-valueequals

nothing

​(Round to three decimal places as​ needed.)

​i) At

alpha

equals0.10

​,

what do you​ conclude?

▼

Fail to reject

Reject

Upper H 0

.

There

▼

is

is not

sufficient evidence to conclude that the advertising lowered the mean number of drunk drivers on the road.

Answer 1

​

a)

Yes, because each day of the week was compared before and after the

advertisement.

b)

mean difference =2.571

c)

Sd =6.079

d)

standard error of the mean difference =2.298

e)

value of the​ t-statistic =1.119

f) degrees of freedom =6

g)option D

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

h)

p value =0.153

i)

Fail to reject , there is not