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Elementary Statistics Test Two topics

by: Morgan Walker

Elementary Statistics Test Two topics Stat 2013

Marketplace > Oklahoma State University > Statistics > Stat 2013 > Elementary Statistics Test Two topics
Morgan Walker
OK State
GPA 3.2

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Topics covered in test two. Chapter four, five and six
Elementary Statistics
Robert Adam Molnar
Study Guide
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This 2 page Study Guide was uploaded by Morgan Walker on Tuesday March 1, 2016. The Study Guide belongs to Stat 2013 at Oklahoma State University taught by Robert Adam Molnar in Winter 2016. Since its upload, it has received 99 views. For similar materials see Elementary Statistics in Statistics at Oklahoma State University.


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Date Created: 03/01/16
Chapter 4 Permutations-choosing things in order, nPr= n! / (n-r)! 5! / (5-2)! =20 Combinations- choosing objects in a group with no specific order, fewer than permutations because order doesn’t matter, nCr= n! / r!(n-r)!, 10! / 3! (10-3)! =120 Chapter 5 Discrete distributions- quantitative variable, finite or countable Continuous distributions- measurable set of possibilities Probability rules for discrete distributions- 1. The probability of any event (E) is a real number between and including 0 and 1 a. 0 ≤ P(E)≤ 1 2. The sum of the probabilities of all outcomes in a sample space is 1 a. P(S)=1 3. If an event cant occur the probability is 0 4. If an event is certain to occur its probability is 1 Expected value / mean for discrete distribution, including computation- expected value is denotated with an “E” and population mean is “mu” or µ. Computed by multiplying the outcome by its probability then adding them all togeather. E(X)= x p + 1 1 … x2 2 n n Variance and standard deviation- technically the formula for variance wont be used but just 2 2 incase ∑[x * P(x)] - µ , standard deviation is the square root of variance. Fair games / lotteries-no lottery is fair expected value is zero. Gambler’s Fallacy-the longer the run of bad luck increases the probability of winning, totally false. Binomial distribution conditions: fixed number of trials, success or failure only two outcomes, trials all independent, probability of success same on each trial Binomial formula-P(x)= nCr (p )(1-p) (n-x1-p is the probability of failure p=40% 1-p= 60% Mean- np Variance- np(1-p) standard deviation- √np(1-p) Chapter 6 Normal distribution parameters- mean  and sd  , N(10,4) Normal distribution properties: symmetric , mean=median=mode Standardized scores (Z-scores)- Z = (X – ) /  Standard normal distribution with mean 0, sd 1- E table or normal distribution table. Using the normal distribution table- if z=-.61 find -.6 on left side of table then count outwards starting at .00 till you get to .01 which will be two times. Normal distribution probabilities- theoretically all numbers are possible but the table goes from -3 to positive 3 Inverse normal problems – given probability, find X X= Z()+find  X Pearson’s coefficient of skewness- needs mean, median and standard deviation book rule- PC= 3(mean-median) / standard deviation sample size rule- |PC|= √13/n Sampling error-difference between the sample statistic and the population parameter Population distribution- in real life this is generally unknown sample/data distribution- known data that has been collected in the problem sampling distribution- theoretical or simulated distribution from multiple samples Conditions for CLT: as the sampling size increases the sample mean tends to be normally distributed around the mean and the standard deviation gets smaller as n gets larger. Regardless of the population distribution model Statement of the Central Limit Theorem: Sampling distribution of the mean has approximately normal distribution, mean , SD  / √n Computing probabilities using CLT- Z = (X – ) / standard error (SE) Standard error is calculated by dividing standard deviation by the square root of n S.E=  / √n


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