Question

A home exercise machine is marketed in three ways: via e-mail, by sending a DVD to prospective customers who access the manufacturer’s website, and via telemarketing. For each marketing approach records are kept regarding how many prospective customers make a purchase. The results are summarized as follows:

	Purchased	Did Not Purchase
Email	5	153
DVD	17	141
Phone	18	140

(a) Do the sample data provide evidence that the proportion of customers who decided to make a purchase is different for different marketing approaches? Set up and perform an appropriate test at the ? = 0.05 level of significance.
(b) If your conclusion in Part (a) was to reject the null hypothesis (and it should be!) then use the Marasculio procedure to determine which proportions are different for which other proportions. Again, use ? = 0.05.

Answer 1

a) H0:  the proportion of customers who decided to make a purchase is not different for different marketing approaches

H1:  the proportion of customers who decided to make a purchase is different for different marketing approaches

Let the los be alpha = 0.05

The observed frequencies are

	Purchased	Did not Purchase	Total
Email	5	153	158
DVD	17	141	158
Phone	18	140	158
Total	40	434	474

The expected frequencies are

	Purchased	Did not Purchase	Total
Email	13.333	144.667	158
DVD	13.333	144.667	158
Phone	13.333	144.667	158
Total	39.999	434.001	474

The chisquare contribution values are

Oi	Ei	(Oi-Ei)^2 /Ei
5	13.333	5.21
153	144.667	0.48
17	13.333	1.01
141	144.667	0.09
18	13.333	1.63
140	144.667	0.15
	Total:	8.57

Degrees of freedom: 2

Test Statistic, X^2: 8.5735
Critical X^2: 5.991471
P-Value: 0.0137

Here chisquare value > chisquare critical value and P-value < alpha 0.05 so we reject H0

Thus we conclude that the proportion of customers who decided to make a purchase is different for different marketing approaches

b) Marasculio procedure:

From the given data

	Email	DVD	Phone	Total
Purchased	5	17	18	40
Not Purchase	153	141	140	434
Total	158	158	158	474

sample propotion 0f Email p1 = 5/158 = 0.0316
sample proportion of DVD p2 = 17/158 = 0.1076
sample proportion of Phone p3 = 18/158 = 0.1139