Unit 12-1

Unit 12-1 - Two-Sample Inference Procedures with Means Suppose we have a population of adult men with a mean height of 71 inches and standard

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Two-Sample Inference Procedures with Means
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Suppose we have a population of adult men with a mean height of 71 inches and standard deviation of 2.6 inches. We also have a population of adult women with a mean height of 65 inches and standard deviation of 2.3 inches. Assume heights are normally distributed. Describe the distribution of the difference in heights between males and females (male- female). Normal distribution with μ x-y =6 inches & σ x-y =3.471 inches
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71 65 Female Male  6 Difference = male - female
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Remember: y x y x μ - = - 2 2 y x y x σ + = - We will be interested in the difference of means, so we will use this to find standard error.
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Do calculator simulation! Do calculator simulation! a) What is the probability that the mean height of 30  men is at most 5 inches taller than the mean height  of 30 women? b) What is the 70th percentile for the difference  (male-female) in mean heights of 30 men and 30  women? 6.332 inches 6.332 inches P((x P((x m – x – x w )< 5) = .0573 )< 5) = .0573
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Two-Sample Procedures with means The goal of these inference procedures is to compare the responses to two treatments two treatments or to compare the characteristics of two populations two populations . We have INDEPENDENT samples from each treatment or population
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Assumptions: Have two SRS’s two SRS’s from the populations or two randomly two randomly assigned assigned treatment groups Samples are independent Both populations are normally distributed Have large sample sizes Graph BOTH sets of data σ σ s s known/unknown
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Formulas Since in real-life, we will NOT NOT know both σ ’s, we will do t-procedures.
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Degrees of Freedom Option 1: use the smaller of the two values n 1 – 1 and n 2 – 1
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This note was uploaded on 12/09/2011 for the course STATS 221 taught by Professor Nielson during the Fall '10 term at BYU.

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Unit 12-1 - Two-Sample Inference Procedures with Means Suppose we have a population of adult men with a mean height of 71 inches and standard

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