Question

A student wants to determine if the population of his state prefers Pepsi to Coke. The estimate
of the population proportion is to be within plus or minus .10, with a 90% level of confidence.
From a previous study in another state, he saw that 353 out of 500 people in that study
preferred Pepsi.

How large of a sample is required?

Answer 1

Solution :

Given that,

= 353/500=0.706

1 - = 1 - 0.706 = 0.294

margin of error = E = 0.10

At 90% confidence level z

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

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

= (1.645 / 0.10)² * 0.706* 0.294

=56.16

Sample size = 56