In a certain region biologists inspected 481 deer taken by h

In a certain region biologists inspected 481 deer taken by hunters; 117 of the deer carried ticks that tested positive for Lyme disease. A 99% confidence interval for the proportion of all deer that carry ticks wih the Lyme disease is about?

A) 0.243 + or - 0.050

B) 0.243 + or - 0.025

C) 0.243 + or - 0.0556

D) 0.243 + or - 0.046

E) 0.243 + or - 0.032

Solution

Proportion of deers = 117 / 481 = 0.2432432...s.d = sqrt [ p(1-p) / n ] = 0.01956257.....
z-score for 99% conf. interval = 2.575829..
margin of error = (2.575829*0.01956257 ) = 0.05038984......
confidence interval = [ 0.2432432- (2.575829*0.01956257 ) , 0.2432432 + (2.575829*0.01956257 ) ]
i.e, A) 0.243 + or - 0.050.....