Suppose a random Sample of size 53 is selected from a popula

Suppose a random Sample of size 53 is selected from a population with sigma = 10. Find the value of the mean in which of the following cases (use the finite correlation factor if appropriate) The population size is finite (to 2 decimals) The population size is N = 50,000(to 2 decimals) The population size is N = 5000(to 2 decimals) The population size is N = 500(to 2 decimals)

Solution

Note that

fpc = sqrt[(N-n)/(N-1)]

and

SE (standard error) = sigma*fpc / sqrt(n)

where

sigma = standard deviation of the population
N = population size
n = sample size

Thus,

a)

As N-->oo, the fpc = 1.

SE = 1.373605639 [ANSWER]

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b)

Here,

fpc = 0.999479854

Thus,

SE = 1.372891164 [ANSWER]

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C)

Here,

fpc = 0.994785364

Thus,

SE = 1.366442785 [ANSWER]

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D)

Here,

fpc = 0.946462669

Thus,

SE = 1.300066459 [ANSWER]