Question

You want to create a 95% confidence interval to estimate the proportion of Americans that like beets. What is the minimum sample size you need to guarantee a margin of error no larger than .05?

Answer 1

Solution:

Here p is not given , hence p = 0.5

C = 95% = 0.95 , α = 1 - C = 0.05 , 1-α/2 = 0.975

Using Normal Table Z1-α/2 = 1.96

Margin of error = E = 0.05

Sample size = n = (Z2)p(1-p)/E2 = ((1.96*1.96)(0.5*0.5))/(0.05*0.05) = 384.16 ~ 385

Answer : 385