12 The heights of 1000 students at a university are normally

12

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]