Question

You wish to estimate the proportion of students in your math class who got a flu vaccine last year. Without taking an initial sample, how many students should you include in your sample to arrive at a 95% confidence interval for the population proportion that has a margin of error of 0.013?

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.013

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= (1.96 / 0.013)² * 0.5 * 0.5

= 5682.84

Sample size =5683