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UW-Madison PSYCH 210 - Sampling Distributions

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BIOM 121 1nd Edition Lecture 10 Outline of Last Lecture Binomial distributionsII. Sampling Distributionsa. Not on first examOutline of Current Lecture I. Continue Sampling Distributionsa. Constructing a Sampling Distributionb. The Central Limit Theoremi. Estimated Mean Valueii. Standard Errorc. Sample Sizei. ‘Law of Large Numbers’Current LectureI. Sampling Distributionsa. Difference btwn Sampling and Sample Distributioni. Sample Distribution1. Distribution from a single sample2. x-axis: x variableii. Sampling Distribution1. x-axis changes from x to M2. Not just a single sample, but multiple samplesb. Construct a Sampling distribution using M&M’s i. All students with M&M’s receive ‘ID number’ii. N=29, n=5, 20 samples (Full sampling distribution would take every possible sample!)These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.iii. Random number generatoriv. Created Sampling distribution1. Resembles Normal Distribution2. Population μ=10. 21: sample means tend to pile up around μa. Normally we will not know μ!b. Mean of Sample means = Expected Mean Value (EMV) =10.48i. When we cannot access entire population, EMV will give us good estimate of population μc. The Central Limit Theoremi. Def: For any population with a mean μ and a standard deviation σ, the sampling distribution of sample means from sample sixe n will approach anormal distribution with a mean of μ and a standard deviation of σ/√n an n approaches infinity1. We have a population2. Each sampling distribution is specific to its sample size3. The sampling distribution will take on the shape of a normal distribution as n gets bigger4. The (full) sampling distribution itself will take on a mean of μ (EMV) and a SD of σ/√na. Standard Errori. Sampling distributions have special Standard Deviations: σM = σ/√nd. What influences standard Error?i. Sample size1. Ex) Attitude toward Binge Drinking (scale)a. Population: Undergraduates @ UW Madisonb. Theoretically have data on entire population (μ = 100, σ = 15)i. n=11. Standard Error σM = 15/√1 = 15a. The amount of mistake you’re making in using EMV to estimate population μ2. 15 = The most our mean could be off byii. n=91. σM = 5iii. n=251. σM = 32. The larger the sample, the more accurately the sample represents its populationa. ‘Law of Large Numbers’e. Ex) Supermax Prisonsi. Super Maximum Security Prisons 1. For the “worst of the worst prisoners”a. Prisoners completely socially isolatedii. Aggression Test1. μ = 500, σ = 1002. “Treatment” – Txa. Live at Supermax for 1yrb. n=25, M=5253. What is the probability of getting a mean aggression score of M>525 just by chance?a. p(M>525)i. z-scores/probability to answer question!1. Type 1ii. Sketch.1. x-axis has M instead of xiii. Convert M to z1. z= (M-μ)/σM a. σM = √σ2/nb. (525-500)/20 = 1.25iv. Look up p on Unit Normal Table1. p =


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UW-Madison PSYCH 210 - Sampling Distributions

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