Question

A college registrar wants to estimate the proportion of all students at the college who are dissatisfied with the online registration procedure. What is the most conservative estimate of the minimum sample size that would limit the margin of error to be within 0.045 of the population proportion for a 95% confidence interval?

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5= 0.5

margin of error = E = 0.045

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025= 1.96 ( Using z table )

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

= (1.96 / 0.045)2 * 0.5 * 0.5

= 474.27

Sample size =474