A supermarket chain wants to know if their "buy one, get one free" campaign increases customer traffic enough to justify the cost of the program. For each of 10 stores they select two days at random to run the test. For one of those days (selected by a coin flip), the program will be in effect. They want to test the hypoth- esis that there is no mean difference in traffic against the alternative that the program increases the mean traffic. Here are the results in number of customer visits to the 10 stores:
|
Store #
|
With Program
|
Without Program
|
|
1
|
140
|
136
|
|
2
|
233
|
235
|
|
3
|
110
|
108
|
|
4
|
42
|
35
|
|
5
|
332
|
328
|
|
6
|
135
|
135
|
|
7
|
151
|
144
|
|
8
|
33
|
39
|
|
9
|
178
|
170
|
|
10
|
147
|
141
|
a) Are the data paired? Explain.
b) Compute the mean difference.
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.
h) What is the P-value associated with this t-statistic? (Assume that the other assumptions and conditions for in- ference are met.)
i) At a = 0.05, what do you conclude?