Question

A.) Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with ? = 2.0%. A random sample of 10 bank stocks gave the following yields (in percents).

5.7

4.8

6.0

4.9

4.0

3.4

6.5

7.1

5.3

6.1

The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is ? = 4.4%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.4%? Use ? = 0.01.
What is the level of significance?

Compute the z value of the sample test statistic. (Round your answer to two decimal places.)

Find (or estimate) the P-value. (Round your answer to four decimal places.)

B.) 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.

At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below.

Weather Station	1	2	3	4	5
January	137	122	128	64	78
April	108	111	100	88	61

Does this information indicate that the peak wind gusts are higher in January than in April? Use ? = 0.01. (Let d = January ? April.)

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

C.) 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 environmental studies, sex ratios are of great importance. Wolf society, packs, and ecology have been studied extensively at different locations in the U.S. and foreign countries. Sex ratios for eight study sites in northern Europe are shown below.

Location of Wolf Pack	% Males (Winter)	% Males (Summer)
Finland	78	55
Finland	68	65
Finland	66	69
Lapland	55	48
Lapland	64	55
Russia	50	50
Russia	41	50
Russia	55	45

It is hypothesized that in winter, "loner" males (not present in summer packs) join the pack to increase survival rate. Use a 5% level of significance to test the claim that the average percentage of males in a wolf pack is higher in winter. (Let

d = winter ? summer.)

What is the level of significance?

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

D.) 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:	12.5	13.4	12.8	12.3	11.4	11.1	14.2	15.1
B:	9.8	14.3	10.5	14.4	13.0	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 ? = 0.01. (Let

d = A ? B.)

What is the level of significance?

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

Answer 1