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 > 0.05 N ), better results can be obtained by using the finite population correction factor, which involves multiplying the margin of error E by ( 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 x ¯ = 0.8565 g and s = 0.0518 g. First construct a 95% confidence interval estimate of μ , 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.
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 > 0.05 N ), better results can be obtained by using the finite population correction factor, which involves multiplying the margin of error E by ( 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 x ¯ = 0.8565 g and s = 0.0518 g. First construct a 95% confidence interval estimate of μ , 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.
Solution Summary: The author explains the 95% confidence interval estimate of mu , assuming that the population is large and the mean weight of M&Ms in the full bag.
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
(
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
x
¯
= 0.8565 g and s = 0.0518 g. First construct a 95% confidence interval estimate of μ, 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.
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
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