Question

Please calculate a confidence interval for the percent of your customers you expect to go unsatisfied. You surveyed 63 customers, from a population of 600 customers, and found that 18% of them were unsatisfied. You wish to be 97% confident when stating this interval range. FPCF

Answer 1

Sample size, n = 63

z value for 97% confidence interval = NORMSINV(1-(1-.97)/2) = 2.17

Mean proportion, $\bar{p}$ = 0.18

Standard deviation, $\sigma$ = sqrt($\bar{p}$*(1-$\bar{p}$)/n)

= sqrt(0.18*(1-0.18)/63)

= 0.0484

97% Confidence interval:

Lower limit = $\bar{p}$ - z*$\sigma$ = 0.18 - 2.17*0.0484 = 0.0750 = 7.5 %

Upper limit = $\bar{p}$ + z*$\sigma$ = 0.18 + 2.17*0.0484 = 0.2850 = 28.5 %