Sample Size with Finite Population Correction Factor The methods of this section assume that sampling is from a population that is very large or infinite, and that we are sampling with replacement. If we have a relatively small population and sample without replacement, we should modify E to include a finite population correction factor, so that the margin of error is as shown in Exercise 37, where N is the population size. That expression for the margin of error can be solved for n to yieldRepeat Exercise 32, assuming that a simple random sample is selected without replacement from a population of 500 people. Does the additional information about the population size have much of an effect on the sample size?Exercise 17Confidence Interval with Finite Population Correction Factor The standard error of the mean is σ/√n, provided that the population size is infinite or very large or sampling is with replacement. If the population size N is finite, then the correction factor √(N – n)/(N – 1) should be used whenever n > 0.05N. The margin of error E is multiplied by this correction factor as shown below. Repeat part (a) of Exercise 25 assuming that the sample is selected without replacement from a population of size 200. How is the confidence interval affected by the additional information about the population size?Exercise 25 SAT Scores A simple random sample of 125 SAT scores has a mean of 1522. Assume that SAT scores have a standard deviation of 333.a. Construct a 95% confidence interval estimate of the mean SAT score.Exercise 32Sample Size for White Blood Cell Count What sample size is needed to estimate the mean white blood cell count (in cells per microliter) for the population of adults in the United States? Assume that you want 99% confidence that the sample mean is within 0.2 of the population mean. The population standard deviation is 2.5.
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