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# Lecture31 - ECO220Y Lecture 31 Inference of Two Populations...

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ECO220Y Lecture 31 CO220 ectu e 3 Inference of Two Populations –Part1 Migiwa Tanaka Reading: 13.1 1

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utline Outline Estimation and hypothesis testing of difference in the means of two populations: μ 1 2 Three Cases: When σ 1 and σ 2 are known When σ 1 and σ 2 are unknown but σ 1 ൌ σ 2 hen nd e unknown and When σ 1 and σ 2 are unknown and σ 1 ് σ 2 Observational Data and Experimental Data revisited ti ti d H th i t ti f diff i th Estimation and Hypothesis testing of difference in the proportions of two populations: p 1 -p 2 2
Inference of Two Populations xample: Gender Gap Example: Gender Gap Do males earn more than females? We can compare the average earnings of males and females from a random sample. .08 Male, mean=21.98,n 1 =1901 Female, mean=18.47,n 2 =1739 Hourly Earnings in the U.S. (age:25-34, 2004) .06 y 2 .04 Densit 0 .0 0 0 0 0 0 0 3 0 20 40 60 Hourly Earnings (\$) 0 20 40 60 Hourly Earnings (\$)

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Inference of Two Populations ore general questions More general questions The question is if these samples are drawn from the populations with the identical mean. Is the difference in the means merely due to sampling error? Or are two samples drawn from inherently different population? Hourly Earnings in the U.S. (age:25-34, 2004) 06 .08 Male, mean=21.98,n 1 =1901 Female, mean=18.47,n 2 =1739 2 .04 .0 Density 0 0 20 40 60 0 20 40 60 4 Hourly Earnings (\$) Hourly Earnings (\$)
ypothesis Hypothesis Do males earn more than females? Let μ 1 mean earnings of male Let μ mean earnings of female 2 H 0 : μ 1 2 =0 H : μ -μ >0 1 1 2 Data: Hourly Earnings in the U.S. in 2004 from the Current Population Survey, of 3,640 working adults between age 25-34. 5

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Inference of difference between μ 1 and μ 2 hen when 1 2 Point Estimator: X X Remember the sampling distribution of If X 1 and X 2 are normal and independent, or 2 1 2 1 X X If X 1 and X 2 are independent and their sample sizes are large
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Lecture31 - ECO220Y Lecture 31 Inference of Two Populations...

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