# chp9 - CHAPTER 9 Homework: 1,6,15,24,47,49,53,57 Sec 9.1:...

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1 CHAPTER 9 Homework: 1,6,15,24,47,49,53,57 Sec 9.1: Sampling Distribution for the difference of two sample means: 1. Sampling distribution for the difference of two independent sample means : (a). The central limit theory ensures that the sampling distribution for the difference of two independent sample means is approximately normal for sufficiently large samples.

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2 (b). The difference of the two sample means is an unbiased estimator for the difference of the two population means. (c). The standard deviation for the difference of two independent sample means is where σ 1 and σ 2 are the population standard deviations and n 1 and n 2 are the respective sample sizes. σ d n n = 1 2 1 2 2 2 +
3 2. Problem of two paired samples Sometimes the two samples are paired. For example, suppose x1, x2, . ., xn are weights of n people before they are enrolled onto a dietary course, and y1,y2,. .,yn are the corresponding weights of these n people after they complete the dietary course. Here the two samples are not independent, because xi and yi are the weights of the same person -- a paired measurements. We call these two samples paired samples . In order to

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4 assess the usefulness of the dietary course, we would be interested in making inference on the mean weight reduction after completing the course, d. For this, we can base our inference on y1-x1, y2- x2,. .,yn-xn, which can be regarded as a random sample taken from the population of weight reduction after completing the course. Therefore the problem is reduced to a one-sample problem which has already been dealt with in chapters 7 and 8. We will not discuss two-paired-sample problem further in this chapter.
5 Sec 9.2: Large sample inference for the difference of two independent population means (1) The confidence interval Under the assumption that two random samples taken independently from two populations have large enough sample sizes, the 1- α confidence interval for difference of the two population means is given by where s d s n s n = 1 2 1 2 2 2 + x x z s d 1 2 2 - ± α /

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6 (2) Hypotheses testing: (a). Alternative Hypothesis: (i). Two-Tailed Test: H a : ( μ 1 2 ) d 0 (ii). Right-Tailed Test: H a : ( μ 1 2 ) d 0 (iii). Left-Tailed Test: H a : ( μ 1 2 ) < d 0 (b). Null Hypothesis: (i). Two-Tailed Test: H 0 : ( μ 1 2 ) = d 0 (ii). Right-Tailed Test: H 0 : ( μ 1 2 ) d 0 (iii). Left-Tailed Test: H 0 : ( μ 1 2 ) d 0
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## This note was uploaded on 08/30/2011 for the course STA 2023 taught by Professor Bagwhandee during the Fall '07 term at University of Central Florida.

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chp9 - CHAPTER 9 Homework: 1,6,15,24,47,49,53,57 Sec 9.1:...

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