Question

A manager of a gym wants to determine the proportion of patrons who use the gym on a regular basis by constructing a 95% confidence interval. If the desired margin of error is 5%, what sample size should the manager use, if a prior estimate of p is 0.8?

Answer 1

Solution :

Given that,

= 0.8

1 - = 1 - 0.8 = 0.2

margin of error = E = 5% = 0.05

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 / 0.05)2 * 0.8 * 0.2

= 245.86

Sample size =246