Question

The Fast N' Hot food chain wants to test if their "Buy One, Get One Free" program increases customer traffic enough to support the cost of the program. For each of 15 stores, one day is selected at random to record customer traffic with the program in effect, and one day is selected at random to record customer traffic with program not in effect. The results of the experiment are documented in DATA. For each store, compute difference = traffic with program minus traffic without program. At x = 0.05, test the hypothesis that the mean difference is at most 0 (at best the program makes no difference, or worse it decreases traffic) against the alternative that the mean difference > 0 (the program increases traffic).

Customer Traffic
With Program	Without Program
136	140
228	233
111	110
38	42
332	332
132	135
150	151
35	33
189	178
141	147
175	162
253	243
144	149
49	48
356	346

Answer 1

Let us denote

d = traffic with program - traffic without program

To test against

Here

sample mean of difference

sample standard deviation of difference

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 0.05 level of significance if P-value < 0.05

Now,

The value of the test statistic

and P-value =

Since P-value > 0.05, so we fail to reject H₀ at 0.05 level of significance and we can conclude that the program significantly increases customer traffic.