Question

Consider a simple poll that is measuring the proportion of citizens that hold a particular political belief. What is a conservative, "worst case scenario" sample size if you want the margin of error to be 4.4%?

Answer 1

When proportion p is unknown, we use formula for sample size.

n =   

Where, n = minimal sample size for a specified confidence level and maximal error estimate.

E = Specified maximal error of estimate.

Zc = Critical value from normal distribution for the desired confidence level.

E= 0.044, We will calculate sample size for confidence level 95% ,zc = z0.95 = 1.96 ( Using standard normal table)

n =

n =

n= 496.0743         (If n is not whole value, consider it to next whole number because n is sample size which must be a whole number)

n= 497

A sample should be 497 for maximum error 0.044 with 95% confidence.

For 99% confidence interval:

E= 0.044, zc = z0.99 = 2.58 ( Using standard normal table)

You can find this z value using excel command “=NORMSINV(0.005)”

n =   

n =   

n= 859.555         (If n is not whole value, consider it to next whole number because n is sample size which must be a whole number)

A sample should be 860 for maximum error 0.044 with 99% confidence.