lec6.7 - 163 Lecture 17 CHAPTER 6: HYPOTHESIS TESTING...

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163 Lecture 17 CHAPTER 6: HYPOTHESIS TESTING Small-Sample Tests for the Difference Between Two Means – Cont’d (Section 6.7, page 430) When the Populations Have Equal Variances Suppose that a srs of size n 1 is drawn from a normal population with unknown mean 1 and that an independent srs of size n 2 is drawn from another normal population with unknown mean 2 . Suppose also that the two populations have the same standard deviation . This suggests the use of a pooled t-test! To test the hypothesis 2 1 : o H , for a pooled t-test, compute the two-sample test statistic 2 1 2 1 2 1 1 1 ) ( n n s x x t p where the degrees of freedom for the pooled t density curve is 2 2 1 n n and the pooled variance is 2 ) 1 ( ) 1 ( 2 1 2 2 2 2 1 1 2 n n s n s n s p Example: Two methods have been developed to determine the nickel content of steel. In a sample of five replications of the first method on a certain kind of steel, the average measurement (in percent) was 16 . 3 x and the standard deviation was 042 . 0 x s . The average of seven replications of the second method was 24 . 3 y and the standard deviation was 048 . 0 y s . Assume that it is known that the population variances are nearly equal. Can we conclude that there is a difference in the mean measurements between the two methods?
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Exercise 6 from text, page 442: Two weights, each labeled as weighing 100g, are each weighed several times on the same scale. The results, in units of g above 100 g, are as follows: First weight: 53 88 89 62 39 66 Second weight: 23 39 28 2 49 Since the same scale was used for both weights, and since both weights are similar, it is reasonable to assume that the variance of the weighing does not depend on the object being weighed. Can you conclude that the weights differ? Hypothesis: Summary Statistics: Use a pooled t-test because it states “. .assume that the variance of the weighing does not depend on the object being weighed”: 2 1 2 1 2 1 1 1 ) ( n n s x x t p where p s P-value: there is ______________ evidence at the 0.05 significance level to conclude a significant difference in the mean weights.
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lec6.7 - 163 Lecture 17 CHAPTER 6: HYPOTHESIS TESTING...

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