In the following data pairs A represents birth rate and B re

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: 11.4 13.4 12.0 12.2 13.2 11.6 14.2 15.1 B: 10.3 9.9 10.7 10.3 13.9 11.1 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 = 0.05.

(a) What is the level of significance?

State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

H_o: _d = 0; H₁: _d 0; two-tailed, H_o: _d 0; H₁: _d = 0; two-tailed    H_o: _d = 0; H₁: _d > 0; right-tailed, H_o: _d = 0; H₁: _d < 0; left-tailed

(b) What sampling distribution will you use? What assumptions are you making?

The Student\'s t. We assume that d has an approximately normal distribution.The standard normal. We assume that d has an approximately normal distribution.    The Student\'s t. We assume that d has an approximately uniform distribution.The standard normal. We assume that d has an approximately uniform distribution.

What is the value of the sample test statistic? (Use 3 decimal places.)


(c) Find (or estimate) the P-value. (Use 4 decimal places.)

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?

At the = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) State your conclusion in the context of the application.

Fail to reject the null hypothesis, there is insufficient evidence to claim that the average birth and death rates are different in this region.Fail to reject the null hypothesis, there is sufficient evidence to claim that the average birth and death rates are different in this region.    Reject the null hypothesis, there is insufficient evidence to claim that the average birth and death rates are different in this region.Reject the null hypothesis, there is sufficient evidence to claim that the average birth and death rates are different in this region.

Solution

The test carried out using MS-EXCEL add-in data analysis gives following results.

(1)

Level of significance : 0.05

Null Hypothesis : H_o: _d = 0;

Alternate Hypothesis : H₁: _d 0;

This is a two tailed test .

(b)

We will use the student\'s t. we assume that the difference d has an approximately normal distribution.

The test statistic\'s value is 1.912.

(c)

The corresponding P-value is 0.0751.

(d)

At the = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e)

Fail to reject the null hypothesis, there is insufficient evidence to claim that the average birth and death rates are different in this region