Question

Suppose a pollster wants to construct a 90% confidence interval. The expectation is that the winning candidate will end up with about 55% of the overall vote. How large should the pollster’s sample size be to ensure their election prediction is within one percent of the actual results?

Answer 1

Solution,

Given that,

= 0.55

1 - = 1 - 0.55 = 0.45

margin of error = E = 0.01

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.645 / 0.01)2 * 0.55 * 0.45

= 6697.41

sample size = n = 6698