Suppose a random sample of size 50 is selected from a popula

Suppose a random sample of size 50 is selected from a population with = 10. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).

Round your answers to two decimal places.

a. The population size is infinite.

b. The population size is N = 50,000.

c. The population size is N = 5000.

d. The population size is N = 500.

Solution

As

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

and

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

where

N = population size
n = sample size

then,

a)

If N = infinity, then fpc = 1.

Thus,

SE = 10*1/sqrt(50) = 1.414213562 = 1.41 [ANSWER]

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b)

If N = 50000, then

fpc = sqrt((50000-50)/(50000-1)) = 0.99950987

Thus,

SE = 10*0.99950987/sqrt(50) = 1.413520414 = 1.41 [ANSWER]

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c)

If N = 5000, then

fpc = sqrt((5000-50)/(5000-1)) = 0.995086951

Thus,

SE = 10*0.995086951/sqrt(50) = 1.407265462 = 1.41 [ANSWER]

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d)

If N = 500, then

fpc = sqrt((500-50)/(500-1)) = 0.949633407

Thus,

SE = 10*0.949633407/sqrt(50) = 1.342984443 = 1.34 [ANSWER]