In: Statistics and Probability
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. The chief of police wants to collect a random sample of traffic stops.
The chief of police wants to estimate the actual proportion of drivers who are stopped that are female.
To calculate the required sample size, what value of p* should we use in the formula below to calculate a 90% confidence interval within 3.02 percentage points? Give exact answer as a decimal.
n=p*(1−p*)(z*ME)2
Solution,
Given that,
= 1 - = 0.5 ( no prior estimate )
margin of error = E = 0.0302
At 90% confidence level
= 1 - 90%
= 1 - 0.90 =0.10
/2
= 0.05
Z/2
= Z0.05 = 1.645
sample size = n = (Z / 2 / E )2 * * (1 - )
= (1.645 / 0.0302)2 * 0.5 * 0.5
= 741.75
sample size = n = 742