Question

Suppose the Bureau of the Census wants to estimate the mean family size for all U.S. families at a 99% confidence level. It is known that the standard deviation σ for the sizes of all families in the United States is .6. How large a sample should the bureau select if it wants its estimate to be within .01 of the population mean?

Answer 1

Solution :

Given that,

standard deviation =s =   =0.6

Margin of error = E = 0.01

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.576

sample size = n = [Z/2* / E] 2

n = ( 2.576* 0.6/ 0.01 )2

n =23888.79

Sample size = n =23889