The heights of 1000 students at a university are normally di

The heights of 1000 students at a university are normally distributed with a standard deviation of 2 inches. If several samples consisting of 36 students are taken, determine the standard deviation of the sample mean under the following conditions. the sampling was done with replacement the sampling was done without replacement

Solution

a)

If with replacement,

SE = s/sqrt(n)

= 2/sqrt(36)

= 0.333333 [ANSWER]

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b)

If without replacement,

SE = s*fpc/sqrt(n)

where

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

Thus,

fpc = sqrt(1000-36)/sqrt(1000-1) = 0.982326303

Thus,

SE = 2*0.982326303/sqrt(36) = 0.327442101 [ANSWER]