Question

4. To determine the effectiveness of a proposed public relations campaign, the senior vice president for customer relations for an automobile manufacturer asked seven consumers how much they liked the company (on a scale from 0 [do not like] to 50 [like very much]) before and after viewing the primary television advertisement of the campaign. Use the following data to test whether the consumers’ ratings of the company increased, on average, after viewing the television advertisement:

	RATING
CONSUMER	Before	After
1	42	49
2	21	15
3	31	35
4	7	13
5	29	41
6	35	39
7	14	22

a. State the null and alternative hypotheses associated with the test.
b. If α = 0.05, what is the critical value of the associated test statistic?
c. What is the calculated value of the associated test statistic?
d. State your decision about the null hypothesis by comparing the critical and calculated values of the test statistic (Parts b and c).
e. Comment on the effectiveness of the primary television advertisement of the campaign.

Answer 1

The table given below ,

Consumer	Before	After	di=After-Before	di^2
1	42	49	7	49
2	21	15	-6	36
3	31	35	4	16
4	7	13	6	36
5	29	41	12	144
6	35	39	4	16
7	14	22	8	64

From table ,

Sample size=n=7

Let ,

Here , use the paired t-test.

Since , the test is right (one) tailed test

a) The hypothesis is given by ,

The alternative hypothesis is  

b) The critical value is given by ,

; ;From t-table

c) The test statistic associated to this test is ,

d) Decision : Here ,

Therefore , reject the null hypothesis

e) Conclusion : Hence , the data provide the sufficient evidence to test the consumers’ ratings of the company increased, on average, after viewing the television advertisement.

Therefore , the primary television advertisement of the campaign is effective.