Question

A national safety council wishes to estimate the proportion of automobile accidents that involve pedestrians. How large a sample of accident records must be examines to be 97% certain that the estimate has a margin of error four percentage points?

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 4% = 0.04

At 97% confidence level the z is ,

= 1 - 97% = 1 - 0.97 = 0.03

/ 2 = 0.03 / 2 = 0.015

Z_/2 = Z_0.015 = 2.17

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

= (2.17 / 0.04)² *0.5*0.5

= 735.77

sample size = 736