1Chapter 8. Sections 8.1 and 8.2 Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

MARIO F. TRIOLAMARIO F. TRIOLA EIGHTHEIGHTH

EDITIONEDITION

ELEMENTARY STATISTICS Chapter 8 Inferences from Two Samples

2Chapter 8. Sections 8.1 and 8.2 Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Chapter 8 Inferences from Two Samples

8-1 Overview

8-2 Inferences about Two Means: Independent and Large Samples

8-3 Inferences about Two Means: Matched Pairs

8-4 Inferences about Two Proportions

8-5 Comparing Variation in Two Samples

8-6 Inferences about Two Means: Independent       and Small Samples

3Chapter 8. Sections 8.1 and 8.2 Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

8-1 Overview

There are many important and meaningful situations in which it becomes necessary

to compare two sets of sample data.

4Chapter 8. Sections 8.1 and 8.2 Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

8-2

Inferences about Two Means:Independent and

Large Samples

5Chapter 8. Sections 8.1 and 8.2 Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Definitions

Two Samples: IndependentThe sample values selected from one population are not related or somehow paired with the sample values selected from the other population.

If the values in one sample are related to the values in the other sample, the samples are dependent. Such samples are often referred to as matched pairs or paired samples.

6Chapter 8. Sections 8.1 and 8.2 Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Assumptions

1. The two samples are independent.

2. The two sample sizes are large. That is,    n1 > 30 and n2 > 30.

3. Both samples are simple random   samples.

7Chapter 8. Sections 8.1 and 8.2 Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Hypothesis Tests

Test Statistic for Two Means: Independent and Large Samples

(x1 - x2) - (µ1 - µ2)z =n1 n2

+1

. 2

22

8Chapter 8. Sections 8.1 and 8.2 Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Hypothesis Tests

Test Statistic for Two Means: Independent and Large Samples

and If and are not known, use s1 and s2 in their places. provided that both samples are large.

P-value: Use the computed value of the test

statistic z, and find the P-value by following the same procedure summarized in Figure 7-8.

Critical values: Based on the significance level , find critical values by using the procedures introduced in Section 7-2.

9Chapter 8. Sections 8.1 and 8.2 Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Coke Versus PepsiData Set 1 in Appendix B includes the weights (in pounds) of samples of regular Coke and regular Pepsi. Sample statistics are shown. Use the 0.01 significance level to test the claim that the mean weight of regular Coke is different from the mean weight of regular Pepsi.

10Chapter 8. Sections 8.1 and 8.2 Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Coke Versus PepsiData Set 1 in Appendix B includes the weights (in pounds) of samples of regular Coke and regular Pepsi. Sample statistics are shown. Use the 0.01 significance level to test the claim that the mean weight of regular Coke is different from the mean weight of regular Pepsi.

Regular Coke Regular Pepsi

n 36 36

x 0.81682 0.82410

s 0.007507 0.005701

11Chapter 8. Sections 8.1 and 8.2 Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Coke Versus Pepsi

12Chapter 8. Sections 8.1 and 8.2 Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Claim: 1 2

Ho : 1 = 2

H1 : 1 2

= 0.01

Coke Versus Pepsi

Fail to reject H0Reject H0Reject H0

Z = - 2.575 Z = 2.5751 - = 0

or Z = 0

13Chapter 8. Sections 8.1 and 8.2 Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Test Statistic for Two Means: Independent and Large Samples

(x1 - x2) - (µ1 - µ2)z =n1 n2

+1

. 2

22

Coke Versus Pepsi

14Chapter 8. Sections 8.1 and 8.2 Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Test Statistic for Two Means: Independent and Large Samples

(0.81682 - 0.82410) - 0z =36

+

Coke Versus Pepsi

0.0075707 2 0.005701 2

36

= - 4.63

15Chapter 8. Sections 8.1 and 8.2 Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Claim: 1 2

Ho : 1 = 2

H1 : 1 2

= 0.01

Coke Versus Pepsi

Fail to reject H0Reject H0 Reject H0

Z = - 2.575 Z = 2.5751 - = 0

or Z = 0

sample data:z = - 4.63

16Chapter 8. Sections 8.1 and 8.2 Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Claim: 1 2

Ho : 1 = 2

H1 : 1 2

= 0.01

Coke Versus Pepsi

Fail to reject H0Reject H0 Reject H0

Z = - 2.575 Z = 2.5751 - = 0

or Z = 0

sample data:z = - 4.63

Reject Null

There is significant evidence to support the claim that there is a difference

between the mean weight of Coke and the mean weight of Pepsi.

17Chapter 8. Sections 8.1 and 8.2 Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Confidence Intervals

(x1 - x2) - E < (µ1 - µ2) < (x1 - x2) + E

18Chapter 8. Sections 8.1 and 8.2 Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Confidence Intervals

(x1 - x2) - E < (µ1 - µ2) < (x1 - x2) + E

n1 n2

+1 2where E = z

22