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# 1/27/2016 Class Notes MAT 258

Andrew
SUNY Oswego
GPA 3.6

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Notes taken in class on 1/27/2016
COURSE
Intro To Statistics B
PROF.
Gregory Schneider
TYPE
Class Notes
PAGES
3
WORDS
KARMA
Free

## Popular in Mathematics (M)

This 3 page Class Notes was uploaded by Andrew on Friday January 29, 2016. The Class Notes belongs to MAT 258 at State University of New York at Oswego taught by Gregory Schneider in Winter 2016. Since its upload, it has received 26 views. For similar materials see Intro To Statistics B in Mathematics (M) at State University of New York at Oswego.

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Date Created: 01/29/16
MAT 258 Gregory Schneider 1/28/2016 Class Notes  This Covers: Section 8.1 o Sampling Distributions: sampling distributions of a statistic give the probability distribution of that statistic for a given sample size  Sample size of 4 was taken from the …lass Name - Height A – 76” M – 71” R – 76” (Ex. of cluster sample) E – 66”  Assume the population: { A,M,R,E } - Avg. height: µ = 289/4 = 72.25” (Population Q: How many mean) different samples of a size of 2?  Order doesn’t matter 4 ! Solution: (4 x 3) / 2 = 6 OR 2! (4-2)! Names - Avg. Height – Probability A, M – 73.5 1/6 A, R – 76 1/3 A, E – 71 1/6 (gives the sampling distribution of average height of sample size of 2 from M, R – 73.5 1/3 the population) M, E – 68.5 1/6 R, E – 71 1/3 Q: What if the population (and sample) are large?  Can’t just count them out like the previous problem. How do we find an easier way to do sampling distribution if it’s a big population? Sample IQ Problem from Text: IQ scores X normally distributed with mean of 100 and standard deviation of 15 2 X ~ N (100, 15 ) Look at sampling dist. for x and n=9 (normalM /µ) (ơ ) X1+ x +2--- + µ = xa 9 Theorem: If distribution of random variable X is normal, with open M and standard deviation ơ, then the sampling distribution of x is normal, with mean µ and standard dev. ơ/ √n √n SE (x) = ơ/ (referred to as standard error of mean) Q: What if the population is not normal?  What if it isn’t centered and it’s nasty lookin like this: Solution: Central Limit Theorem – If X has any probability distribution, then the sampling distribution of x becomes normal as sample size n increases. (the bigger n is, the more centered and normal looking the curve becomes) Q: How large does n have to be?  According to text: 30. This is true for the most part Probabilities Involving Sample Mean  Avg. American male is 70” tall with st. dev. of 3” Took sample of 50 males. What is probability that avg. height is ≥ 71” X ~ N (70, 3”) OR n = 50 ≥ 30 √50 2  x ~ N (70, [3/ ] )  P (x ≥ 71) = 1-P (x ≤ 71) √50  = 1-P (Z ≤ 71-70/[3/ ] )  = 1-P (Z ≤ 2.36)  = 1 – 0.9909 = Go to tables at end of 0.0091 book to find 0.9909 SE = ơ/ √n

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