Question

In a study of perception, 108 men are tested and 12 are found to have red/green color blindness.

(a)	[2 marks] Find a 91% confidence interval for the true proportion of men from the sampled population that have this type of color blindness.

(b)	[2 marks] Using the results from the above mentioned survey, how many men should be sampled to estimate the true proportion of men with this type of color blindness to within 3% with 96% confidence?

Answer 1

Solution :

Given that,

a) Point estimate = sample proportion = = x / n = 12 / 108 = 0.11

1 - = 1 - 0.11 = 0.89

Z/2 = Z_0.045 = 1.695

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.695 (((0.11 * 0.89) / 108)

= 0.051

A 91% confidence interval for population proportion p is ,

± E   

= 0.11 ± 0.051

= ( 0.059, 0.161 )

b) Z/2 = Z_0.02 = 2.054

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (2.054 / 0.03)² * 0.11 * 0.89

= 458.92

sample size = n = 459