Additional Estimation Topics noteshells

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Unformatted text preview: 1 Additional Estimation Topics 1 Additional Estimation Topics Sections 8.7, 8.5 And elsewhere Additional Estimation Topics 2 Intervals for Population Mean μ In our previous lecture, we looked at intervals for the population mean. Our estimate came from: where t is a value from the t-distribution with n-1 degrees of freedom and is the approximate standard error. n s t X ± n s 2 Additional Estimation Topics 3 Assumptions In forming this interval, we made some implicit assumptions: 1. We wanted to estimate the average value in the population of interest, and not some function of it; 2. The population was infinite in size or the sample was only a small fraction of the population; and 3. The observations in this population were normally distributed. Additional Estimation Topics 4 Deviation from assumptions h Assumption (2): The population was infinite in size or the sample was only a small fraction of the population. h If we sample a large portion of a population with known size N, theory shows that the usual standard error estimate is too large. h There is a “finite population correction” we can apply to get a narrower interval. 3 Additional Estimation Topics 5 The Finite Population Correction h Theory is in Section 8.7, which is an “Online Topic” in our textbook. h You can download this from the Chapter 8 materials at the textbook companion website: http://wps.prenhall.com/bp_levine_statsexcel_6/ h Use a t-distribution interval with the corrected standard error: where the ^ on σ means “estimated”. 1 ˆ-- = N n N n s X σ Additional Estimation Topics 6 Example h In 2005, the Survey of Current Business (U.S. Bureau of the Census) contains 492 cities of at least 50,000 residents. h We have a sample of 41 cities and want to estimate the average percentage of individuals living under the poverty level. h Data in CitySample.xls which is on the course E-learning site. 4 Additional Estimation Topics 7 Example (continued) n = 41 and N = 492 Sample average is 15.63 Sample s.d. is 6.295 Additional Estimation Topics 8 In PhStat 5 Additional Estimation Topics 9 Notes on FPC h Some texts say to apply it only when the sampling fraction f = n/N is at least .05 (when you sample at least 5% of the population)....
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This note was uploaded on 02/14/2011 for the course QMB 3250 taught by Professor Thompson during the Spring '08 term at University of Florida.

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Additional Estimation Topics noteshells - 1 Additional...

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