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Statistics Test 3 Study Guide

by: Erik Arnold Bloomgren

Statistics Test 3 Study Guide Econ 210

Marketplace > University of North Dakota > Economcs > Econ 210 > Statistics Test 3 Study Guide
Erik Arnold Bloomgren
GPA 2.9

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Covers ch.6-8
Intro to bus & economic statistic
Kristopher Paulson
Study Guide
50 ?




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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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