Suppose a simple random sample of size 55 is selected from a

Suppose a simple random sample of size 55 is selected from a population with =8. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).

a. The population size is infinite (to 2 decimals)

b. the population size is N = 50,000 (to 2 decimals)

c. The population size is N = 5,000 (to 2 decimals)

d. The population size is N = 500 (to 2 decimals)

Solution

Note that

standard error = sigma*fpc/ sqrt(n)

where

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

a)

Here,

fpc = 1 as N-->infinity.

Thus,

standard error = 8(1)/sqrt(55) = 1.07871978 [ANSWER]

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b)

If N = 50000,

fpc = 0.999459843

Thus,

standard error = 8(0.999459843)/sqrt(55) = 1.078137102
[ANSWER]

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c)

If N = 5000,

fpc = 0.994584255

Thus,

standard error = 8(0.994584255)/sqrt(55) = 1.072877708 [answer]

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d)

If N = 5000,

fpc = 0.944342929

standard error = 8(0.944342929)/sqrt(55) = 1.018681396 [answer]