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Solution of Chapter 10: Statistics for Business by Andersen Sweeney Williams

In: Business and Management

Submitted By sakettiwari
Words 4104
Pages 17
Chapter 10 Statistical Inference about Means and Proportions with Two Populations
Learning Objectives 1. Be able to develop interval estimates and conduct hypothesis tests about the difference between two population means when σ 1 and σ 2 are known. Know the properties of the sampling distribution of x1 − x2 . Be able to use the t distribution to conduct statistical inferences about the difference between two population means when σ 1 and σ 2 are unknown. Learn how to analyze the difference between two population means when the samples are independent and when the samples are matched. Be able to develop interval estimates and conduct hypothesis tests about the difference between two population proportions. Know the properties of the sampling distribution of p1 − p2 .

2. 3.

4. 5. 6.

10 - 1

Chapter 10

Solutions: 1. a. b. x1 − x2 = 13.6 - 11.6 = 2 zα / 2 = z.05 = 1.645

x1 − x2 ± 1.645

σ 12 n1 +

2 σ2

n2

2 ± 1.645

(2.2) 2 (3) 2 + 50 35

2 ± .98 c.

(1.02 to 2.98)

zα / 2 = z.025 = 1.96
2 ± 1.96 (2.2) 2 (3) 2 + 50 35

2 ± 1.17 2. a. z= (.83 to 3.17)
= (25.2 − 22.8) − 0 (5.2) 2 62 + 40 50 = 2.03

( x1 − x2 ) − D0 σ 2 1

n1

+

σ

2 2

n2

b. c. 3. a.

p-value = .5000 - .4788 = .0212 p-value ≤ .05, reject H0. z= ( x1 − x2 ) − D0 σ 2 1

n1

+

σ

2 2

=

(104 − 106) − 0 (8.4) 2 (7.6) 2 + 80 70

= −1.53

n2

b. c. 4. a.

p-value = 2(.5000 - .4370) = .1260 p-value > .05, do not reject H0. x1 − x2 = 2.04 - 1.72 = .32 z.025

b.

σ 12 n1 +

2 σ2

n2

1.96

(.10)2 (.08) 2 + = 1.96(.0208) = .04 40 35

c.

.32 ± .04

(.28 to .36)

10 - 2

Statistical Inference about Means and Proportions with Two Populations x1 − x2 = 14.9 - 10.3 = 4.6 years zα / 2

5.

a.

b. c. 6.

σ 12 n1 +

2 σ2

n2

= 1.96

(5.2) 2 (3.8) 2 + = 1.3 100 85

4.6 ± 1.3...

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