INTRODUCTORY STATISTICS CH 7.1-7.4 NOTES
INTRODUCTORY STATISTICS CH 7.1-7.4 NOTES MATH 10041-007
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This 0 page Class Notes was uploaded by Marissa Nichol on Thursday November 5, 2015. The Class Notes belongs to MATH 10041-007 at Kent State University taught by Xianglan Bai in Summer 2015. Since its upload, it has received 22 views. For similar materials see INTRODUCTORY STATISTICS in Math at Kent State University.
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Date Created: 11/05/15
INTRODUCTORU STATISTICS CH 7 7172 characterizes population through a numerical value sample of data represented by a numerical value also known as a statistic estimate value of an estimator 2 Examples of an estimator sampe proportion p hat symbol sample mean x with bar symbol artscience of drawing a conclusion based on infostats of a population measures the performance of a method which is bias if it s tendency is to produce untrue values 3 TYPES OF BIAS Natural bias Sampling bias amp measurement bias convenience sampling voluntary sampling non sampling sampling stat naturally bias not producing a true answer to a question Bias measured as DISTANCE between center value of estimator amp population parameter drawing people randomly from a population without replacement of sampling survey measured by precision of estimator Quality measured using standard error of sampling distribution when small estimator is precise The size of population doesn t effect precision of estimator p hat called the sampling distribution of the sample proportion Sampling distribution relays values of p hat amp their probabilities Phat symbol sample proportion amp used to estimate population proportion 73 The sample proportion is normally distributed when there is a big sample size no matter how the population is divided The answer is better with the increase of sample size so the normal distribution is used to nd probabilities of sample proportion 3 conditions Central Limit Theory 1 Random and independent 2 Large sample 3 Big population ten times bigger than sample size at least 4 If sample is picked randomly from population the sample proportion unbiasedhas the standard error SE SE square root of p times 1p divided by n sample 5 CLT if sampling distribution is Normal mean population proportion mu phat Standard deviaton square root of phat1phatn sigma phat 6 Unbiased estimator sample statistic unbiased estimator if the value of estimator the same as population parameter 7 Consisten estimator is Standard Deviation a sample statistic decreases amp sample size increases The central limit theorem for sample proportions when trials are randomindependent amp samplepopulation sizes large sampling distributions phat is normal amp follors Np square root of p1pn standard deviation same as standard error SE when you don t know p then phat can be substituted to nd standard error mean 48200 024 SEest square root of 24 x 76200 about 03 74 mu p value sigma SE 2 x bar musigmazphat p hat pSE SE square root of 081084000 0045 2 090800429 233
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