Question

In hopes of improving Mrs. Puppet’s image as a candidate for mayor, her campaign manager Mr. Strings created a commercial. Before airing the commercial, he hires your consulting firm to determine if the commercial would actually improve voters’ attitudes toward Mrs. Puppet. As a first step, your firm conducts a very small pilot study to help those who will collect the data to understand the experimental procedures. The firm wants to make sure the experimental procedures are well understood before it doles out all the cash needed for the large study. The firm obtains a sample of 10 undecided voters to participate in the study. First, each voter rated their current feelings toward Mrs. Puppet by answering several questions such as the following:

1-Definitely would not vote for her                       9-Definitely would vote for her                     

  1 2 3    4    5    6    7    8    9

Then, all participants watched the commercial and answered all of the preceding questions a second time. Obviously, if the commercial works, approval ratings should be higher after voters view the commercial.

1. What are the null and alternative hypotheses?
2. What is the one-tailed critical t value for this study?
3. Using the table on the next page, complete a paired samples t-test by hand for the data.

Should you reject the null hypothesis or not?

            t =                                df =                                         p =

4. Calculate Cohen’s d. How big is the effect?

Previewing	Postviewing	Difference (D)
4	5
3	5
3	4
5	5
4	6
4	5
6	7
2	3
4	4
5	7
Mpre = 4.00 SDpre = 1.15	Mpost = 5.10 SDpost = 1.29	Mdifference = SDdifference =

Answer 1

The hypothesis being tested is:

H₀: µ_d = 0

H_a: µ_d < 0

Previewing	Postviewing	Difference (D)
4	5	-1
3	5	-2
3	4	-1
5	5	0
4	6	-2
4	5	-1
6	7	-1
2	3	-1
4	4	0
5	7	-2
	Mdifference =	-1.100
	SDdifference =	0.738
	4.000	mean Previewing
	5.100	mean Postviewing
	-1.100	mean difference (Previewing - Postviewing)
	0.738	std. dev.
	0.233	std. error
	10	n
	9	df
	-4.714	t
	.0005	p-value (one-tailed, lower)

The one-tailed critical t value for this study is 2.685.

t = -4.714 df = 9 p = 0.0005

The p-value is 0.0005.

Since the p-value (0.0005) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the commercial works, approval ratings should be higher after voters view the commercial.