An investigator is interested in estimating the total weight gain over a 4 week

Question

An investigator is interested in estimating the total weight gain over a 4 week period for N = 1000 chicks fed a new diet using 95% confidence interval. To weigh each bird would be tedious and time consuming, so a simple random sample will be used instead. Determine the sample size required in this study in order to estimate the total weight gain with a bound on the error of estimation equal to 1000 grams. Similar studies on chick nutrition have been conducted in the past showing that the population variance of weigh gain is 36 grams.

Explanation / Answer

nere N=1000, variance=36 and sd=sqrt(36)=6, let sample size =n

with (1-alpha)*100% confidence margin of error of population total= z(alpha/2)*sqrt(n)*sd

with 95% confidence margin of error of population total= z(alpha/2)*sqrt(n)*sd

1000=1.96*sqrt(n)*6

or, sqrt(n)=1000/(6*1.9*)=87.72

or, n=7694.67 ( next integer=7695)

n=7695

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