Question

In a study of perception, 143 men are tested and 24 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 1% with 97% confidence?

Answer 1

Solution :

Given that,

a) Point estimate = sample proportion = = x / n = 24 / 143 = 0.168

1 - = 11 - 0.168 = 0.832

Z/2 = Z0.045 = 1.70

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

= 1.70 (((0.168 * 0.832) / 143)

= 0.053

A 91% confidence interval for population proportion p is ,

± E  

= 0.168  ± 0.053

= ( 0.115, 0.221 )

b)   Z/2 = Z0.015 = 2.17

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

= (2.17 / 0.01)2 * 0.168 * 0.832

= 6581.91

sample size = n = 6582