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VCU STAT 210 - Lecture37(3)

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Slide 1Test 6 ResultsPractice ProblemsAdditional Reading and ExamplesSlide 5Statistical InferenceStatistical InferenceExample 1Example 1Example 2Example 2Motivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleMotivating ExamplePoint EstimateSampling DistributionSampling DistributionSampling DistributionSampling DistributionSampling DistributionSampling DistributionSampling DistributionSampling DistributionSampling DistributionSampling DistributionExample 96Example 96Example 96Example 96Example 96Example 96Example 96Example 96Example 96Example 96Example 96Example 96Example 97Example 97Example 97Example 97Example 97Example 97Example 97Example 97Example 97Example 97Example 97Sampling DistributionZ-Score TransformationFinding ProbabilitiesExample 98Example 98Example 98Example 98Example 98Example 98Example 99Example 99Example 99Example 99Example 99Motivating ExampleMotivating ExampleMotivating Example SolutionSee you Wednesday!STAT 210Lecture 37 Sampling Distribution of X1 – X2November 28, 2016Test 6 ResultsMean: 75.9 Median: 83Max: 100 Min: 3 n: 120Score Frequency Relative Frequency90’s 42 35.00%80’s 27 22.50%70’s 19 15.83%60’s 9 7.50% <60 23 19.17%Practice ProblemsPages 286 through 291Relevant problems: X.1 and X.2Recommended problems: X.1 and X.2Additional Reading and ExamplesRead pages 281 through 283ClickerStatistical InferenceStatistical inference involves using statistics computed from sample data to make statements about unknown population parameters.This includes estimation (confidence intervals) and significance tests.In the past two chapters we made inferences about the population mean m and about the population proportion p.Statistical InferenceNow suppose we have two populations with population means m1 and m2, respectively, and of interest is to make statistical inferences about the difference between the two population means: m1 - m2.Example 1It is of interest to estimate the difference in the mean IQ of all male students at this university and the mean IQ of all female students at this university. Populations of interest: ???Parameter of interest: ???Example 1It is of interest to estimate the difference in the mean IQ of all male students at this university and the mean IQ of all female students at this university. Then the populations of interest are all male students at this university and all female students at this university, and the parameter of interest is m1 - m2 = the difference between the mean IQ of all male students (m1) and the mean IQ of all female students (m2).Example 2The economic downturn of 2008 and 2009 did not affect all people equally. It is conjectured that the mean loss in investments among all people who live in urban settings was different from the mean loss in investments among all people who live in rural settings. Populations of interest: ???Parameter of interest: ???Example 2The economic downturn of 2008 and 2009 did not affect all people equally. It is conjectured that the mean loss in investments among all people who live in urban settings was different from the mean loss in investments among all people who live in rural settings. Then the populations of interest are all people who live in urban settings and all people who live in rural settings, and the parameter of interest is m1 - m2 = the difference between the mean loss in investments among all people who live in urban settings (m1) and the mean loss in investments among all people who live in rural settings (m2).Motivating ExampleThe Main Event of the 2016 World Series of Poker concluded on October 30 through November 1 (shown live on ESPN). 6,737 players paid $10,000 each to enter the event, and the winner, Qui Nguyen, received $8,005,310.Of interest is to compare the mean number of hands played by all professional players to the mean number of hands played by all amateur players.Motivating ExampleThe Main Event of the 2016 World Series of Poker concluded on October 30 through November 1 (shown live on ESPN). 6,737 players paid $10,000 each to enter the event, and the winner, Qui Nguyen, received $8,005,310.Of interest is to compare the mean number of hands played by all professional players to the mean number of hands played by all amateur players.What are the populations of interest?Motivating ExampleThe Main Event of the 2016 World Series of Poker concluded on October 30 through November 1 (shown live on ESPN). 6,737 players paid $10,000 each to enter the event, and the winner, Qui Nguyen, received $8,005,310.Of interest is to compare the mean number of hands played by all professional players to the mean number of hands played by all amateur players.What are the populations of interest?The populations include all professional players in the 2016 World Series of Poker Main Event and all amateur players in the 2016 World Series of Poker Main Event.Motivating ExampleThe Main Event of the 2016 World Series of Poker concluded on October 30 through November 1 (shown live on ESPN). 6,737 players paid $10,000 each to enter the event, and the winner, Qui Nguyen, received $8,005,310.Suppose we want to estimate the difference in the mean number of hands played by all professional players and the mean number of hands played by all amateur players.What is the parameter of interest?Motivating ExampleThe Main Event of the 2016 World Series of Poker concluded on October 30 through November 1 (shown live on ESPN). 6,737 players paid $10,000 each to enter the event, and the winner, Qui Nguyen, received $8,005,310.Suppose we want to estimate the difference in the mean number of hands played by all professional players and the mean number of hands played by all amateur players.What is the parameter of interest?The parameter of interest is m1 – m2 = the difference in the mean number of hands played by all professional players and the mean number of hands played by all amateur players.Point EstimateOnce the populations and the parameter are identified, samples are selected from the populations. We take a simple random sample of n1 subjects from the first population and also a simple random sample of n2 subjects from the second population. From each sample we compute the sample means, X1 and X2. Then the point estimate of m1 - m2 is the difference in the sample means: X1 - X2.The samples could be selected independently of each other, or they could be dependent. There are different procedures that depend on whether the samples are


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VCU STAT 210 - Lecture37(3)

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