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## MSIT UNIT 9 – Sampling Distributions & Confidence Intervals for Proportions

by: Katie Mulliken

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0

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# MSIT UNIT 9 – Sampling Distributions & Confidence Intervals for Proportions MSIT 3000

Marketplace > University of Georgia > Statistics > MSIT 3000 > MSIT UNIT 9 Sampling Distributions Confidence Intervals for Proportions
Katie Mulliken
UGA
GPA 3.91

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MSIT UNIT 9 – Sampling Distributions & Confidence Intervals for Proportions Includes: parameter, stimulations, sampling distribution, standard error, normal modal, independence assumption (10% ...
COURSE
PROF.
Megan Lutz
TYPE
Class Notes
PAGES
2
WORDS
CONCEPTS
samplingdistribution, confidenceinvervals, confidencelevels, parameter, stimulation, standarderror, normalmodal, independenceassumption, marginoferror
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## Popular in Statistics

This 2 page Class Notes was uploaded by Katie Mulliken on Tuesday October 11, 2016. The Class Notes belongs to MSIT 3000 at University of Georgia taught by Megan Lutz in Summer 2015. Since its upload, it has received 3 views. For similar materials see Statistical Analysis for Business in Statistics at University of Georgia.

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Date Created: 10/11/16
MSIT UNIT 9 – Sampling Distributions & Confidence Intervals for Proportions p – true proportion of success  in a pop. is constant; parameter pp  –the sample proportion of  Parameter (fixed)of a population is the proportion of success in a succes(relative frequency) population (we can observe a sample, but probably won’t find the true value of the parameter) n – sample size P np  –expected # successes P (sample statistic) does change & a sampling distribution shows us how nq  –expected # failures Stimulations – helps understand what other samples & instances of p would be p EX: Roll a 6-sided dice 5 times. Let {1,2} be a success & all else be a failure (p = 1/3 ) Find p p(the sample proportion of successes of rolling a dice x5): Say a stimulation & observes the following: P Avg. p pppx. = .3 Range: {0:1} P 0 .2 .4 .6 .8 1.0 True proportion = 1/3 (# of successes) X 0 1 2 3 4 5 Mean (typical valueof pp= p With more repetitions (long-run) the distribution of S: unimodal & roughly symmetric  nearly normal Sampling Distribution – the distribution of a sample statistic Standard Error of a sample statistic is its distribution’s Standard Deviation. Standard Error of p: Sp {p} p SE {p}p = √p(1-p) ÷ n = √pq ÷ n Normal Model is ONLY used under specific sampling assumptions & conditions: 1) Independence Assumption: the trials must be independent of one another a. Randomization Condition: data from an experiment study must have randomly chosen subjects If data via survey, must have used SRS or an unbiased sampling methods b. 10% Condition: if a population is finite (small enough) you shouldn’t sample more than 10% 2) Sample Size Assumption: to use the normal appx., sample size (n) must be satisfyingly large. a. Success / Failure Condition: we need “n” big enough to get at least 10 successes + 10 failures expected in the population: np) & nq are both > 10 Confidence Intervals (CI) We know, based on the sampling distribution of S, that the long-run avg. of p = p p (the true proportion) We want to know, based on our current sample if p = p…. p Note: P(p =pp) = 0 Confidence Interval – a range of volume, or an interval of #s, calculated from sample data that can be used to estimate a population proportion. Confidence Level – a value chosen to represent the confidence in our statistical method (not in our data) CI = pp̂ + z*√pp̂ qp̂ ÷n pp+ ( Critical Value x Standard Error ) OR pp+ Margin of Error A higher Margin of Error arises when: More confidence in an interval = Bigger z* = Smaller “n” is = Bigger size = More narrow/ precise

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