Question

# In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of...

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
 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 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 = AB.)

(a) What is the level of significance?

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

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)

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