?Finite Population Correction Factor If a simple random sample of size n is selected

Chapter 7, Problem 39

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Finite Population Correction Factor If a simple random sample of size n is selected without replacement from a finite population of size N, and the sample size is more than 5% of the population size (n > 0.05N), better results can be obtained by using the finite population correction factor, which involves multiplying the margin of error E by \(\sqrt{(N-n) /(N-1)}\). For the sample of 100 weights of M&M candies in Data Set 27 “M&M Weights” in Appendix B, we get \(\bar{x}=0.8565 \mathrm{~g}\) and s = 0.0518 g. First construct a 95% confidence interval estimate of \(\mu\), assuming that the population is large; then construct a 95% confidence interval estimate of the mean weight of M&Ms in the full bag from which the sample was taken. The full bag has 465 M&Ms. Compare the results.

Text Transcription:

sqrt (N-n)/(N-1)

bar x=0.8565

mu