Question

Police stops ~ The Minneapolis Police Department records data on all traffic stops made by their police officers such as race, gender, reason, citation issued, etc. To estimate the proportion of drivers who are stopped that are female, the chief of police takes a random sample of 94 traffic stops and finds that in 22 of them, the driver was female.

Using this data, the chief of police wants to estimate the actual proportion of drivers who are stopped that are female.

What is the required sample size to calculate a 95% confidence interval within 3.11 percentage points? Use z*=1.96.

n=p*(1−p*)(z*ME)2

Answer 1

Solution :

Given that,

= X / n = 0.23

1 - = 0.77

margin of error = E = 0.0311

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

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

= (1.96 / 0.0311)2 * 0.23 *0.77

= 703.41

sample size = 704