Statistics Test 3 Study Guide
Statistics Test 3 Study Guide Econ 210
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Erik Arnold Bloomgren
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This 3 page Study Guide was uploaded by Erik Arnold Bloomgren on Saturday March 26, 2016. The Study Guide belongs to Econ 210 at University of North Dakota taught by Kristopher Paulson in Winter 2016. Since its upload, it has received 21 views. For similar materials see Intro to bus & economic statistic in Economcs at University of North Dakota.
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Date Created: 03/26/16
Test 3 Study Guide Statistics New Stats Symbols Z – tells standard deviation from xvalue to zvalue in Standard Normal Distribution, also called standard normal variable σxbar Standard error of mean P – Population proportion σpbar Standard error of proportion t – tells of t distribution when standard deviation for population (σ) is UNKNOWN E – desired margin of error CH. 6 Terms Uniform Probability Distribution – a rectangle curve with sides a and b Uniform Probability Density Function – f(x)=1/(ba); f(x) is height Expected Value of Uniform Continuous Probability Distribution – E(x)=(a+b)/2 Variance of Uniform Continuous Probability Distribution – Var(x)=(ba) /12 Normal Probability Distribution – a bell curve Normal Curve Characteristics µ=tallest height; total area under curve is 1; mean, median, and mode are all equal; Larger σ, shorter and longer the distribution Standard Normal Random Variable – z Exponential Probability Distribution – decreasing exponential curve Exponential Probability Distribution Density Function – (1/µ)*e^(x/µ) Exponential Distribution Probabilities – P(x≤x )=1e^ox /µ)—givos area to the left; P(x≤x )oe^(x /µo—gives area to the right; Exponential Distribution tells length of interval between occurrences while Poisson Distribution tells number of occurrences per interval NOTE: when P(x=any number)=0 because no area under curve CH. 7 Terms Simple Random Sample – the n of sample randomly selected Point Estimation – xbar or pbar, use data from sample to compute a value of a sample statistic that serves as an estimate of a population parameter Sampling Distribution of xbar – standard normal distribution; z=(xbar µ)/σ xbar Expected Value of xbar – E(xbar)=µ Standard Deviation of xbar – σ xbar first decision, know N?, No then equation is σ x =σ/√n; Yes then another decision, n/N≤5%?, Yes then σ = σ/√n, No then bar xbar σ xbar[(Nn)/(N1)]*σ/√n Sample Correction Factor when standardizing a variable (Zscore formula adjustment) – z=(xµ)/σ xbaror z=(p pbar)/σ pbar Sampling Distribution of pbar – Standard Normal Distribution Expected Value of pbar – E(pbar) = p Standard Deviation of pbar – σ pbar,irst decision, know N?, No then equation is σ p =√p(1p)/(n); Yes, then another decision, n/N≤5%?, Yes then σ =√p(1p)/(n), No then bar pbar σ pbar[p(1p)/(n)]*√[(Nn)/(N1)] Continuous for pbar to be an estimate using a normal distribution np≥5 and n*(1p)≥5 Types of Sampling – Stratified Random Sampling, Cluster Sampling, Systematic Sampling, Convenience Sampling, and Judgement Sampling CH. 8 Terms Interval Estimation Population Mean Known – xbar+orz *(σ/√n) α/2 Steps in Calculating the Interval Estimation with Population Standard Deviation Known (σ) – 1. α/2=(1confedence)/2 so conf. +(α/2)= area under curve 2. Find area in ztable 3. use zvariable in calculation Margin of Error – the +or number found or z *(σ/√n) α/2t *(s/√n) α/2 Interval Estimation Population Mean Unknown – xbar+or t *(s/√n) α/2 Steps in calculating the interval estimation with population standard deviation unknown – 1. α/2=(1confedence)/2 so (α/2)= area under curve in upper tail 2. Find area in ttable by degrees of freedom (n1) and α/2 3. Calculate s=√(Σ(xixbar)/(n1)) 4. Plug into s and t into equation α/2 Determining sample size – n=((z ) σ )/α/2 E= z *(σ/√n) α/2 Population Proportion Interval Estimation – pbar+orz *√pbar(1α/2bar)/(n) Determining Sample size for a proportion – n=((z ) p*(1p*α/2E ), p* = best guess or .5 E=z α/2bar(1pbar))/(n)
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