Lecture Business statistics in practice (7/e): Chapter 11 - Bowerman, O'Connell, Murphree

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Chapter 11 - Statistical inferences for population variances. After mastering the material in this chapter, you will be able to: Explain the basic terminology and concepts of experimental design, compare several different population means by using a one-way analysis of variance, compare treatment effects and block effects by using a randomized block design,...

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Nội dung Text: Lecture Business statistics in practice (7/e): Chapter 11 - Bowerman, O'Connell, Murphree

Chapter 11 Statistical Inferences for Population Variances McGrawHill/Irwin Copyright © 2014 by The McGrawHill Companies, Inc. All rights reserved.
Statistical Inferences for Population Variances 11.1 The ChiSquare Distribution 11.2 Statistical Inference for a Population Variance 11.3 The F Distribution 11.4 Comparing Two Population Variances by Using Independent Samples 112
LO11-1: Describe the properties of the chi- square distribution and 11.1 The ChiSquare Distribution use a chi-square table. Sometimes make inferences using the chi square distribution ◦Denoted ² Skewed to the right Exact shape depends on the degrees of freedom ◦Denoted df  A chisquare point ²α is the point under a chi square distribution that gives righthand tail area 113
LO11-2: Use the chi- square distribution to make statistical inferences about population variances. 11.1 Statistical Inference for Population Variance If s2 is the variance of a random sample of n measurements from a normal population with variance σ2 The sampling distribution of the statistic (n 1) s2 / σ2 is a chisquare distribution with (n – 1) degrees of freedom Can calculate confidence interval and perform hypothesis testing 100(1α)% confidence interval for σ2 114
LO11-2 Formulas 2 A 100(1 ) percent confidence interval for is (n 1) s 2 (n 1) s 2 2 , 2 /2 1 /2 2 2 We can test H 0 : 0 at using the test statistic 2 n 1 s2 2 0 115
LO11-3: Describe the properties of the F distribution and use on 11.3 F Distribution F table. Figure 11.5 116
LO11-3 F Distribution Tables The F point F is the point on the horizontal axis under the curve of the F distribution that gives a righthand tail area equal to The value of F depends on a (the size of the righthand tail area) and df1 and df2 Different F tables for different values of ◦Tables A.6 for = 0.10 ◦Tables A.7 for = 0.05 ◦Tables A.8 for = 0.025 ◦Tables A.9 for = 0.01 117
LO11-4: Compare two population variances when the samples are independent. 11.4 Comparing Two Population Variances by Using Independent Samples  Population 1 has variance σ12 and population 2 has variance σ22  The null hypothesis H0 is that the variances are the same ◦ H0: σ12 = σ22  The alternative is that one is smaller than the other ◦ That population has less variable measurements ◦ Suppose σ12 > σ22 ◦ More usual to normalize  Test H0: σ12/σ22 = 1 vs. σ12/σ22 > 1 118
LO11-4 Comparing Two Population Variances Continued  Reject H0 in favor of Ha if s12/s22 is significantly greater than 1  s12 is the variance of a random of size n1 from a population with variance σ12  s22 is the variance of a random of size n2 from a population with variance σ22  To decide how large s12/s22 must be to reject H0, describe the sampling distribution of s12/s22  The sampling distribution of s12/s22 is the F distribution 119