Copyright 2013 Pearson Education, Inc. All rights reserved Chapter 8 Inferences Based on a Single Sample Tests of Hypothesis Copyright 2013 Pearson Education, Inc. All rights reserved 8.1 The Elements of a Test of Hypothesis 8 - 3 Copyright 2013 Pearson Education, Inc.. All rights reserved. Definition 8 - 4 Copyright 2013 Pearson Education, Inc.. All rights reserved. Definition 8 - 5 Copyright 2013 Pearson Education, Inc.. All rights reserved. Definition 8 - 6 Copyright 2013 Pearson Education, Inc.. All rights reserved. Definition 8 - 7 Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.1 The sampling distribution of, Assuming = 2,400 8 - 8 Copyright 2013 Pearson Education, Inc.. All rights reserved. Definition 8 - 9 Copyright 2013 Pearson Education, Inc.. All rights reserved. Definition Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.2 Location of the test statistic for a test of the hypothesis H 0 : = 2,400 Copyright 2013 Pearson Education, Inc.. All rights reserved. Definition Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.3 Location of test statistic when = 2,430 Copyright 2013 Pearson Education, Inc.. All rights reserved. Table 8.1 Copyright 2013 Pearson Education, Inc.. All rights reserved. Procedure Copyright 2013 Pearson Education, Inc.. All rights reserved. Procedure Copyright 2013 Pearson Education, Inc. All rights reserved 8.2 Formulating Hypotheses and Setting Up the Rejection Region Copyright 2013 Pearson Education, Inc.. All rights reserved. Procedure Copyright 2013 Pearson Education, Inc.. All rights reserved. Definition Copyright 2013 Pearson Education, Inc.. All rights reserved. Definition Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.4 Rejection regions corresponding to one- and two tailed tests Copyright 2013 Pearson Education, Inc.. All rights reserved. Table 8.2 Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.5 Two-tailed rejection region: =.01 Copyright 2013 Pearson Education, Inc. All rights reserved 8.3 Test of Hypothesis about a Population Mean: Normal (z) Statistic Copyright 2013 Pearson Education, Inc.. All rights reserved. Procedure Copyright 2013 Pearson Education, Inc.. All rights reserved. Definition Copyright 2013 Pearson Education, Inc.. All rights reserved. Definition Copyright 2013 Pearson Education, Inc.. All rights reserved. Table 8.3 Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.6 MINITAB descriptive statistics for fill amounts, Example 8.4 Copyright 2013 Pearson Education, Inc. All rights reserved 8.4 Observed Significance Levels: p-Values Copyright 2013 Pearson Education, Inc.. All rights reserved. Definition Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.7 Finding the p-value for an upper- tailed test when z = 2.12 Copyright 2013 Pearson Education, Inc.. All rights reserved. Procedure Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.8 Finding the p-value for an one- tailed test Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.9 Finding the p-value for an two- tailed test; p-value = 2(p/2) Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.10 SAS test of mean response time, Example 8.5 Copyright 2013 Pearson Education, Inc.. All rights reserved. Procedure Copyright 2013 Pearson Education, Inc.. All rights reserved. Table 8.4 Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.11 MINITAB lower-tailed test of mean LOS, Example 8.6 Copyright 2013 Pearson Education, Inc.. All rights reserved. Procedure Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure SIA8.1 MINITAB test of = 60 for KLEENEX survey Copyright 2013 Pearson Education, Inc. All rights reserved 8.5 Test of Hypothesis about a Population Mean: Students t-Statistic Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.12 Two-tailed rejection region for small-sample t-test Copyright 2013 Pearson Education, Inc.. All rights reserved. Procedure Copyright 2013 Pearson Education, Inc.. All rights reserved. Definition Copyright 2013 Pearson Education, Inc.. All rights reserved. Table 8.5 Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.13 A t-distribution with 9 df and the rejection region for Example 8.7 Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.14 MINITAB analysis of 10 emission levels, Example 8.7 Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.15 The observed significance level for the test of Example 8.7 Copyright 2013 Pearson Education, Inc.. All rights reserved. Procedure Copyright 2013 Pearson Education, Inc. All rights reserved Large-Sample Test of Hypothesis about a Population Proportion 8.6 Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.16 Rejection region for breast cancer example Copyright 2013 Pearson Education, Inc.. All rights reserved. Procedure Copyright 2013 Pearson Education, Inc.. All rights reserved. Definition Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.17 Rejection region for Example 8.9 Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.18 The observed significance level for Example 8.10 Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.19 MINITAB lower-tailed test of p, Example 8.10 Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure SIA8.2 MINITAB test of p =.5 for KLEENEX survey Copyright 2013 Pearson Education, Inc. All rights reserved Calculating Type II Error Probabilities: More about (Optional) 8.7 Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.20 Values of and for various values of Copyright 2013 Pearson Education, Inc.. All rights reserved. Procedure Copyright 2013 Pearson Education, Inc.. All rights reserved. Procedure (contd) Copyright 2013 Pearson Education, Inc.. All rights reserved. Procedure Copyright 2013 Pearson Education, Inc.. All rights reserved. Procedure (contd) Copyright 2013 Pearson Education, Inc.. All rights reserved. Definition Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.21 Calculation of for drug- injected rate (Example 8.11) Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.22 MINITAB power analysis for Example 8.11 Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.23 Relationship between , , and n Copyright 2013 Pearson Education, Inc.. All rights reserved. Definition Copyright 2013 Pearson Education, Inc. All rights reserved Test of Hypothesis about a Population Variance (Optional) 8.8 Copyright 2013 Pearson Education, Inc.. All rights reserved. Table 8.6 Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.24 Rejection region for Example 8.12 Copyright 2013 Pearson Education, Inc.. All rights reserved. Figure 8.25 SAS test of fill amount variance, Example 8.12 Copyright 2013 Pearson Education, Inc.. All rights reserved. Procedure Copyright 2013 Pearson Education, Inc.. All rights reserved. Definition