Question

Suppose 51% of politicians are lawyers. If a random sample of size 723 is selected, what is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by greater than 4%? Round your answer to four decimal places.

Answer 1

population proportion ,p=   0.51                      
n=   723                      
                          
std error , SE = √( p(1-p)/n ) =    0.0186                      
                          
P ( |p̂ -p| > 0.04 ) =2*P(Z > ( p̂ - p )/SE) =2*P(Z> ( 0.04 ) /    0.0186 ) = 2*P(Z >   2.152   ) = 2*0.0157 =0.0314
  

the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by greater than 4% is 0.0314