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M ARIO F . T RIOLA

S TATISTICS. E LEMENTARY. Chapter 8 Inferences from Two Samples. M ARIO F . T RIOLA. E IGHTH. E DITION. 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

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M ARIO F . T RIOLA

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  1. STATISTICS ELEMENTARY Chapter 8 Inferences from Two Samples MARIO F. TRIOLA EIGHTH EDITION

  2. 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 Chapter 8 Inferences from Two Samples

  3. There are many important and meaningful situations in which it becomes necessary to compare two sets of sample data. 8-1 Overview

  4. 8-2 Inferences about Two Means:Independent and Large Samples

  5. Two Samples: Independent The 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. Definitions

  6. 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. Assumptions

  7. Test Statistic for Two Means: Independent and Large Samples Hypothesis Tests (x1- x2) - (µ1 - µ2) z= 1. 2 2 2 + n2 n1

  8. Test Statistic for Two Means: Independent and Large Samples Hypothesis Tests  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.

  9. Data 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. Coke Versus Pepsi

  10. Data 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 Coke Versus Pepsi

  11. Coke Versus Pepsi

  12. Claim: 12 Ho : 1 = 2 H1 : 12  = 0.01 Coke Versus Pepsi Fail to reject H0 Reject H0 Reject H0 Z = - 2.575 Z = 2.575 1 -  = 0 or Z = 0

  13. Test Statistic for Two Means: Independent and Large Samples Coke Versus Pepsi (x1- x2) - (µ1 - µ2) z= 1. 2 2 2 + n2 n1

  14. Test Statistic for Two Means: Independent and Large Samples Coke Versus Pepsi (0.81682 - 0.82410) - 0 z= 0.005701 2 0.0075707 2 + 36 36 = - 4.63

  15. Claim: 12 Ho : 1 = 2 H1 : 12  = 0.01 Coke Versus Pepsi Reject H0 Reject H0 Fail to reject H0 Z = - 2.575 Z = 2.575 1 -  = 0 or Z = 0 sample data: z = - 4.63

  16. Claim: 12 Ho : 1 = 2 H1 : 12  = 0.01 Coke Versus Pepsi 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. Reject H0 Reject H0 Fail to reject H0 Reject Null Z = - 2.575 Z = 2.575 1 -  = 0 or Z = 0 sample data: z = - 4.63

  17. Confidence Intervals (x1- x2) - E < (µ1 - µ2) < (x1- x2) + E

  18. Confidence Intervals (x1- x2) - E < (µ1 - µ2) < (x1- x2) + E 2 1 2 2 whereE = z + n2 n1

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