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Unformatted text preview: 1 Chapter 8: Statistical Inference: Estimation for Single Populations Sada Soorapanth Spring 2010 2 Statistical Inference: s) (parameter , , Population p ) (statistic , , x Sample p s p p s , , estimate to , , x Calculate Select a random sample Process of Inferential Statistics 3 Statistical Estimation Point estimate  the single value of a statistic calculated from a sample which is used to estimate a population parameter Interval Estimate  a range of values within which the analyst can declare, with some confidence, the population parameter lies. 4 Margin of Error and the Interval Estimate Each week JC department store selects a sample of 100 customers in order to learn about the amount spent per shopping trip (x). Based on historical data, the population standard deviation of amount spent was estimated at $25. X 9 5 % of 9 . 4 96 . 1 = x X 4.9 4.9 ) 5 . 2 , ( ~ = x Normal x 5 100 (1  )%Confidence Interval to estimate when is known Point estimate of Interval estimate of with 100(1 )% confidence level n x x n i i = = 1 n z x n z x or n z x 2 / 2 / 2 / +  6 What does a 95% Confidence Interval actually mean? X 95% X X X X X X 7 Distribution of Sample Means for 100(1 )% Confidence Interval X 1  Z 2 Z 2 Z 2 2 8 Distribution of Sample Means for (1 )% Confidence X Z 2 Z 2 Z 2 2 .5 2 .5 2 9 Example: Distribution of Sample Means for 99% Confidence Interval .495 .495 X 99% .005 .005 Z 2.5762.576 10 Example: (from Black et al) A random sample of 81 items is taken, producing a sample mean of 47. The population standard deviation is 5.89. What is the point estimate of the population mean. Construct a 90% confidence interval to estimate the population mean. 11 Your Turn: (from Black et al) A random sample of size 70 is taken from a population that has a variance of 49. The sample mean is 90.4. What is the point estimate of ? Construct a 94% confidence interval for . 12 Finite population correction factor 100 (1  )%Confidence Interval to estimate for finite population (when is known) N = Population size 1 1 2 / 2 / +  N n N n z x N n N n z x 13 Example: (from Black et al) A random sample of size 39 is taken from a population of size 200 members. The sample mean is 66 and the population standard deviation is 11. Construct a 96% confidence interval to estimate the population mean. What is the point estimate of the population mean? 14 100 (1  )%Confidence Interval to estimate when is unknown Use the sample standard deviation s as a point estimate of ....
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This note was uploaded on 09/10/2011 for the course DS 212 taught by Professor Saltzman during the Spring '08 term at S.F. State.
 Spring '08
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