Question

The new governor wants to estimate the number of legally intoxicated drivers on a certain stretch of highway. How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 4%.

Answer 1

Solution :

Given that,

= 1 - = 0.5

margin of error = E = 4% = 0.04

  At 90% confidence level the z is,

= 1 - 90%

= 1 - 0.90 = 0.10

/2  = 0.05

Z_/2 = Z _0.05 = 1.645

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

= ( 1.645 / 0.04 )² * 0.5 * 0.5

= 422.81

sample size = n = 423