Question

A political candidate has asked you to conduct a poll to determine what percentage of people support her.

If the candidate only wants a 7% margin of error at a 90% confidence level, what size of sample is needed?

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 7% = 0.07

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645} ( Using z table )

Sample size = n = (Z_/2 / E)² * * (1 - )

= (1.645 / 0.07)² * 0.5 * 0.5

=138.0625

Sample size = 138