By Lannaccone R.
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I-22. 17. Fig. I-23. Introduction 30 18. Fig. I-24. 19. Fig. I-25. Introduction 31 I-7 Introduction Summary LARGE SAMPLE INFERENCES ABOUT A SINGLE MEAN ‘‘Large sample,’’ when making inferences about a single population mean, is taken to mean that the sample size n > 30. The sample mean, x , is a point estimate or a single numerical estimate for the population mean, . The interval estimate is a better estimate because it gives the reliability associatedpwith ﬃﬃﬃ the estimate. A (1 À ) conﬁdence interval estimate for is (x Æ z=2 s= n ).
1-2. 35 CHAPTER 1 Two-Sample Inferences 36 where ðn1 À 1ÞS21 þ ðn2 À 1ÞS22 ¼ n1 þ n2 À 2 The test statistic, t, is known to have a student t distribution with n1 þ n2 À 2 degrees of freedom. The two sample variances are pooled because the population variances are assumed equal. The subscript 1 identiﬁes males and the subscript 2 identiﬁes females. S2pooled Note: Zero is put into the test statistic for 1 À 2 because we always assume the null hypothesis to be true. This is the same as saying that 1 ¼ 2.
Clicking OK produces the dialog box shown in Fig. 1-16, which is filled in as shown. 0095. Compare this to the value given in the Minitab output in Fig. 1-14. CHAPTER 1 Two-Sample Inferences Fig. 1-15. Fig. 1-16. 49 CHAPTER 1 Two-Sample Inferences 50 1-6 Exercises for Chapter 1 1. In a recent USA Today snapshot entitled ‘‘Auto insurance bill to jump,’’ the following averages (Table 1-2) were reported. Table 1-2 Average annual consumer spending on auto insurance. 1995 1996 1997 1998 1999 2000 2001 2002 2003 $668 $691 $707 $704 $683 $687 $723 $784 $885 A research study compared 1995 and 2004 by sampling 50 auto insurance payments for these two years.
[Article] Semiparametric models and inference for biomedical time series with extra-variation by Lannaccone R.