In this problem, assume that the distribution of differences is approximately no

Question

In this problem, assume that the distribution of differences is approximately normal. In the following data pairs, A represents birth rate and 8 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. Do the data indicate a difference (either way) between population average birth rate and death rate in this region? Use alpha = 0.01. (Let d = A - B.) (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? (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that d has an approximately uniform distribution. 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. What is the value of the sample test statistic? (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to

Explanation / Answer

Answer:

Sample test statistic =2.293

P=0.0367

Paired t Test

Data

Hypothesized Mean Difference

0

Level of significance

0.01

Intermediate Calculations

Sample Size

16

DBar

1.8875

Degrees of Freedom

15

SD

3.2928

Standard Error

0.8232

t Test Statistic

2.2929

Two-Tail Test

Lower Critical Value

-2.9467

Upper Critical Value

2.9467

p-Value

0.0367

Do not reject the null hypothesis

Paired t Test

Data

Hypothesized Mean Difference

0

Level of significance

0.01

Intermediate Calculations

Sample Size

16

DBar

1.8875

Degrees of Freedom

15

SD

3.2928

Standard Error

0.8232

t Test Statistic

2.2929

Two-Tail Test

Lower Critical Value

-2.9467

Upper Critical Value

2.9467

p-Value

0.0367

Do not reject the null hypothesis

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