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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