Question

If you want to be 99% confident of estimating the population proportion to within a sampling error of ± 0.05 and there is historical evidence that the population proportion is approximately 0.37, what sample size is needed?

A sample size of is needed.

(Round up to the nearest integer.)

Answer #1

Solution :

Given that,

= 0.37

1 - = 1 - 0.37 = 0.63

margin of error = E = 0.05

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.05

Z_{/2}
= Z _{0.005} = 2.576

sample size = n = (Z_{
/ 2} / E )^{2} *
* (1 -
)

= (2.576 / 0.05)^{2} * 0.37 * 0.63

= 619

sample size = **619**

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