商务统计相关知识英文版

1、商务统计相关知识英文版Chapter 8Interval EstimationPopulation Mean: s KnownPopulation Mean: s UnknownDetermining the Sample SizePopulation Proportion A point estimator cannot be expected to provide the exact value of the population parameter. An interval estimate can be computed by adding and subtracting a marg

2、in 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 parameter.Margin of Error and the Interval Estimate The general form of an interval estimate of a population m

3、ean is Margin of Error and the Interval Estimateto find out two positive numbers and , the latter lying between 0 and 1, such that the probability that the randomInterval contains the true parameter is 1- The random interval is Confidence intervalSuch an interval, if it exists, is known as a confide

4、nce interval; 1 is known as the confidence coefficient; and (0 5 and n(1 p) 5./2/2Interval Estimationof a Population ProportionNormal Approximation of Sampling Distribution of Samplingdistribution of p1 - of all valuesInterval EstimateInterval Estimationof a Population Proportionwhere: 1 - is the co

5、nfidence coefficient z/2 is the z value providing an area of /2 in the upper tail of the standard normal probability distribution is the sample proportionPolitical Science, Inc. (PSI) specializes in voterpolls and surveys designed to keep political officeseekers informed of their position in a race.

6、 Using telephone surveys, PSI interviewers askregistered voters who they would vote for if theelection were held that day. Interval Estimationof a Population ProportionExample: Political Science, Inc.In a current election campaign, PSI has just foundthat 220 registered voters, out of 500 contacted,

7、favor aparticular candidate.PSI wants to develop a 95% confidence interval estimate for the proportion of the population ofregistered voters that favor the candidate.Interval Estimationof a Population ProportionExample: Political Science, Inc.where: n = 500, = 220/500 = .44, z/2 = 1.96Interval Estim

8、ationof a Population ProportionPSI is 95% confident that the proportion of all votersthat favor the candidate is between .3965 and .4835.= .44 + .0435Solving for the necessary sample size, we getMargin of ErrorSample Size for an Interval Estimateof a Population ProportionHowever, will not be known u

9、ntil after we have selected the sample. We will use the planning valuep* for .Sample Size for an Interval Estimateof a Population ProportionThe planning value p* can be chosen by:1. Using the sample proportion from a previous sample of the same or similar units, or2. Selecting a preliminary sample a

10、nd using the sample proportion from this sample.Necessary Sample SizeSuppose that PSI would like a .99 probabilitythat the sample proportion is within + .03 of the population proportion.How large a sample size is needed to meet the required precision? (A previous sample of similar units yielded .44 for the sample proportion.)Sample Size for an Interval Estimateof a Population ProportionAt 99% confidence, z.005 = 2.576. Recal