Question

A marketing consultant was hired to visit a random sample of five sporting goods stores across Canada. Each store was part of a large franchise of sporting goods stores. The consultant taught the managers a better way to advertise and display their goods. The net sales for 1 month before, and 1 month after the consultant’s visit were recorded as follows for each store (in thousands of dollars):

Store	1	2	3	4	5
Before visit	57.1	94.6	49.2	77.4	43.2
After visit	63.5	101.8	57.8	81.2	41.9

a) Is this sampling method dependent or independent?

b) State the null and alternate hypotheses to test whether the average net sales improved after the consultants’ visit.

c) Calculate the test statistic. Show calculation.

d) Run the appropriate test in Minitab. Show output. What is the p-value for the test?

e) What are the assumptions for this test? Are the assumptions met?

f) Based on the p-value, interpret the results of this test at a 5% level of significance.

Answer 1

Ans:

a)dependent samples

b)Let d=after-before

	Before	After	d
1	57.1	63.5	6.4
2	94.6	101.8	7.2
3	49.2	57.8	8.6
4	77.4	81.2	3.8
5	43.2	41.9	-1.3
		mean=	4.94
		std. dev=	3.901

c)

Test statistic:

t=(4.94-0)/(3.901/sqrt(5))

t=2.832

d)df=5-1=4

p-value=tdist(2.832,4,1)=0.0236

e)difference of two samples are normally distributed.

f)As,p-value<0.05,we reject the null hypothesis.

There is sufficient evidence to conclude that  the average net sales improved after the consultants’ visit.