商务与经济统计ppt第8章课件

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1、,Click to Edit Master Title Style,Click to edit Master text styles,Second Level,Third Level,1,Slide,2011 Cengage Learning.All Rights Reserved.May not be scanned,copied,or duplicated,or posted to a publicly accessible website,in whole or in part.,Statistics for Businessand Economics,Anderson Sweeney

2、Williams,Slides by,John Loucks,St.Edwards University,Statistics for Businessand Ec,Chapter 8Interval Estimation,Population Mean:,s,Known,Population Mean:,s,Unknown,Determining the Sample Size,Population Proportion,Chapter 8Interval EstimationP,A point estimator cannot be expected to provide the,exac

3、t value of the population parameter.,An,interval estimate,can be computed by adding and,subtracting a,margin of error,to the point estimate.,Point Estimate +/,-,Margin of Error,The purpose of an interval estimate is to provide,information about how close the point estimate is to,the value of the par

4、ameter.,Margin of Error and the Interval Estimate,A point estimator cannot be e,The general form of an interval estimate of a,population mean is,Margin of Error and the Interval Estimate,The general form of an interv,Interval Estimate of a Population Mean:,s,Known,In order to develop an interval est

5、imate of a population mean,the margin of error must be computed using either:,the population standard deviation,s,or,the sample standard deviation,s,s,is rarely known exactly,but often a good estimate can be obtained based on historical data or other information.,We refer to such cases as the,s,know

6、n,case.,Interval Estimate of a Populat,There is a 1,-,probability that the value of a,sample mean will provide a margin of error of,or less.,/2,/2,1-,of all,values,Sampling,distribution,of,Interval Estimate of a Population Mean:,s,Known,There is a 1-probab,/2,/2,1-,of all,values,Sampling,distributio

7、n,of,-,-,-,interval,does not,include,m,interval,includes,m,interval,includes,m,Interval Estimate of a Population Mean:,s,Known,/2/21-of allSampling-,Interval Estimate of,m,Interval Estimate of a Population Mean:,s,Known,where:is the sample mean,1-,is the confidence coefficient,z,/2,is the,z,value pr

8、oviding an area of,/2 in the upper tail of the standard,normal probability distribution,s,is the population standard deviation,n,is the sample size,Interval Estimate of mInterval,Interval Estimate of a Population Mean:,s,Known,Values of,z,a,/2,for the Most Commonly Used Confidence Levels,90%.10 .05

9、.9500 1.645,Confidence Table,Level,a,a,/2 Look-up Area z,a,/2,95%.05 .025 .9750 1.960,99%.01 .005 .9950 2.576,Interval Estimate of a Populat,Meaning of Confidence,Because 90%of all the intervals constructed using,will contain the population mean,we say we are 90%confident that the interval,includes

10、the population mean,m,.,We say that this interval has been established at the,90%,confidence level,.,The value.90 is referred to as the,confidence,coefficient,.,Meaning of Confidence We say,Interval Estimate of a Population Mean:,Known,Example:Discount Sounds,Discount Sounds has 260 retail outlets t

11、hroughout,the United States.The firm is evaluating a potential,location for a new outlet,based in part,on the mean,annual income of the individuals in the marketing,area of the new location.,A sample of size,n,=36 was taken;the sample,mean income is$41,100.The population is not,believed to be highly

12、 skewed.The population,standard deviation is estimated to be$4,500,and the,confidence coefficient to be used in the interval,estimate is.95.,Interval Estimate of a Populat,95%of the sample means that can be observed,are within,+,1.96 of the population mean,.,The margin of error is:,Thus,at 95%confid

13、ence,the margin of error,is$1,470.,Interval Estimate of a Population Mean:,Known,Example:Discount Sounds,95%of the sample means that c,Interval estimate of,is:,Interval Estimate of a Population Mean:,Known,We are,95%confident,that the interval contains the,population mean.,$41,100,+,$1,470,or,$39,63

14、0 to$42,570,Example:Discount Sounds,Interval estimate of is:Int,Interval Estimate of a Population Mean:,Known,90%3.29 78.71 to 85.29,Confidence Margin,Level of Error Interval Estimate,95%3.92 78.08 to 85.92,99%5.15 76.85 to 87.15,Example:Discount Sounds,In order to have a higher degree of confidence

15、,the margin of error and thus the width of the,confidence interval must be larger.,Interval Estimate of a Populat,Interval Estimate of a Population Mean:,s,Known,Adequate Sample Size,In most applications,a sample size of,n,=30 is,adequate.,If the population distribution is highly skewed or,contains

16、outliers,a sample size of 50 or more is,recommended.,Interval Estimate of a Populat,Interval Estimate of a Population Mean:,s,Known,Adequate Sample Size(continued),If the population is believed to be at least,approximately normal,a sample size of less than 15,can be used.,If the population is not normally distributed but is,roughly symmetric,a sample size as small as 15,will suffice.,Interval Estimate of a Populat,Interval Estimate of a Population Mean:,s,Unknown,If an estimate of the population