Lecture_25,_Chap_11,_Sec_2

Lecture_25,_Chap_11,_Sec_2 - Chapter 11 Section 2 Inference...

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Chapter 11 Section 2 Inference about Two Means: Independent Samples
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Two Means – Independent Samples Two samples are independent if the values in one have no relation to the values in the other A typical example of an independent samples test is to test whether a new drug, Drug N, lowers cholesterol levels more than the current drug, Drug C A group of 100 patients could be chosen The group could be divided into two groups of 50 using a random method If we use a random method (such as a simple random sample of 50 out of the 100 patients), then the two groups would be independent
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Two Means – Independent Samples The test of two independent samples is very similar, in process, to the test of a population mean The only major difference is that a different test statistic is used We will discuss the new test statistic through an analogy with the hypothesis test of one mean
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Two Means – Independent Samples Learning objectives Test claims regarding the difference of two independent means Construct and interpret confidence intervals regarding the difference of two independent means 1 2
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Two Means – Independent Samples In the test of two means, we have two values for each variable – one for each of the two samples The two hypothesized means μ 1 and μ 2 The two sample sizes n 1 and n 2 The two sample means x 1 and x 2 The two sample standard deviations s 1 and s 2 ● We expect that x 1 – x 2 would be close to μ 1 – μ 2
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Two Means – Independent Samples For the test of two means, to measure the deviation from the null hypothesis, it is logical to take (x 1 – x 2 ) – (μ 1 – μ 2 ) which has a standard deviation of approximately 2 2 2 1 2 1 n s n s +
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Two Means – Independent Samples Thus for the test of two means, under certain appropriate conditions, the difference (x 1 – x 2 ) – (μ 1 – μ 2 ) is approximately Student’s t with mean 0, and the test statistic has an approximate Student’s t-distribution 2 2 2 1 2 1 2 1 2 1 n s n s ) ( ) x x ( t + - - - = μ
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Two Means – Independent Samples This is Welch’s approximation, that
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This note was uploaded on 08/04/2008 for the course STAT 250 taught by Professor Sims during the Spring '08 term at George Mason.

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Lecture_25,_Chap_11,_Sec_2 - Chapter 11 Section 2 Inference...

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