NOTES_Lecture 19_Continuous Probability Distributions

NOTES_Lecture 19_Continuous Probability Distributions - •...

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11/10/11 Quiz 2 Question 4 causality Lecture 19: Topic Parameters of Sampling Distribution of Sample Mean o As sample size goes up sampling size goes down o Small sampling error helps us make an inference about statistical inference Central Limit Theorem o Sample size should be at least 30 to be conservative o However, possible to get away with less Slide 4 o Average is less variable than a single sample by itself Slide 5 o Normal distribution o As sample size goes up the triangle shape morphs into the bell shape o Reduces standard error, less sampling noise, better inferences Slide 7 o Shape would stay the same, replicate the population distribution o Sample size 100 – shape would be bell-shaped o Slide 8 o Less negatively skewed Student Opinions: Keller 8 ed. o Must be between 0 – 100, negative skew is possible, it could be bimodal o But don’t actually know o P(X-bar = 68) would equal 0 Slide 10 o Sample error doesn’t explain the sample mean of 68
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Unformatted text preview: • Standardize and Use Table o More/less than 3 standard deviations aren’t realistic o Sampling error is not a plausible explanation for low sample mean Non-sampling error Selection-bias, or lying about parameters • Sales Training Example o We don’t know what the shape is, but it doesn’t matter according to the Central Limit Thoerem o Expected mean to increase by 15 but not standard deviation o Slide 18 Sampling distribution of the difference of the means Sampling error can’t explain the difference • Difference Between Two Means o Combining bell-shaped distributions gives another bell-shaped distribution o As long as it is a linear combination • Mean and Variance of Sampling Distribution of Difference o In order for the difference of the two to be bell-shaped, both means need to independently produce a bell-shaped distribution...
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NOTES_Lecture 19_Continuous Probability Distributions - •...

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