Question

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

In the following data pairs, A represents birth rate and B represents death rate per 1000 resident population. The data are paired by counties in the Midwest. A random sample of 16 counties gave the following information.

A:	12.7	13.2	12.6	12.3	11.6	11.1	14.2	15.1
B:	9.8	14.3	10.5	14.2	13.2	12.9	10.9	10.0

A:	12.5	12.3	13.1	15.8	10.3	12.7	11.1	15.7
B:	14.1	13.6	9.1	10.2	17.9	11.8	7.0	9.2

Do the data indicate a difference (either way) between population average birth rate and death rate in this region? Use α = 0.01. (Let d = A − B.)

(a) What is the level of significance?

(b) What is the value of the sample test statistic? (Round your answer to three decimal places.)

Answer 1

Solution :

A	B	d = A - B
12.7	9.8	2.9
13.2	14.3	-1.1
12.6	10.5	2.1
12.3	14.2	-1.9
11.6	13.2	-1.6
11.1	12.9	-1.8
14.2	10.9	3.3
15.1	10	5.1
12.5	14.1	-1.6
12.3	13.6	-1.3
13.1	9.1	4
15.8	10.2	5.6
10.3	17.9	-7.6
12.7	11.8	0.9
11.1	7	4.1
15.7	9.2	6.5

a)

Level of Significance α = 0.01

b)

Test Statistic :

t = 1.175

P-value = 0.25831

P-value > 0.01

Fail to reject H0 (Null hypothesis)