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Intro Stats Week 9

Means instead of the proportion of ilries cornells

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Unformatted text preview: variables With quantitative variables, we are now looking at means Instead of the proportion of ILRies (Cornell’s sexiest major) in the class, think about the mean number of ILRies (Cornell’s sexiest major) in the class Still can use the normal model! Check assumptions and conditions State the parameters and the sampling distribution model Make a picture by sketching the model and shading the area we’re interested in Use the standard deviation as a rule to find the z-score of the cutoff position Use a computer program, table or calculator to find the resulting probability, then interpret it in context of the question The fundamental theorem of statistics! Explaining the CLT ◦ The sampling distribution of any mean becomes more nearly Normal as the sample size grows. All we need is for the observations to be independent and collected with randomization. We don’t even care about the shape of the population distribution! The The CLT ◦ The mean of a random sample is a random variable whose sampling distribution can be approximated by a Normal model. The larger the sample, the better the approximation will be. 2 10/30/2011 Same assumptions as modeling proportions ◦ Independence Assumption ◦ Sample Size Assumption Think about if Independence is plausable, and check related conditions ◦ Randomization Condition: Data values must be sampled randomly, or concept makes no sense ◦ 10% Condition n no more than 10% of population if Condition: drawing without replacement ◦ Large Enough Sample Condition Think about Condition: sample size in the context of the population Think about the assumptions and check the conditions State the parameters and the sampling model Make a picture Use the standard deviation as a ruler to find the z-score and cutoff Use computer program to find probability and interpret result in proper context A confidence interval for a proportion tells us about the sampling distribution of the sample proportion If we don’t know p, we use what we do know (p-hat) ◦ Whenever we estimate the standard deviation of a sampling distribution, we call it a sampling error We know that for 95% of random samples, phat will be no more than 2 SEs away from p Don’t know true value, but can compute an interval that probably contains the true value When a random sample is drawn from any population with mean mu and standard deviation sigma, its sample mean, y-bar, ha...
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