The total number of hate crimes reported for the year 2012 for all 50 states inc

Question

The total number of hate crimes reported for the year 2012 for all 50 states including the District of Columbia was 5796. A researcher randomly selected victims of hate crimes from the original 11 southern states, that is, Louisiana, Alabama, Georgia, Florida, South Carolina, North Carolina, Texas, Virginia, Arkansas, Tennessee, and Mississippi in 2012 and found that there were 884 hate crimes reported in those 11 states alone. Construct a 95% confidence interval for the proportion of hate crimes reported in the original southern states in the year 2012.

Explanation / Answer

here estimated proportion p=884/5796=0.1525

n=5796

therefore std error =(p(1-p)/n)1/2 =0.0047

for 95% confidence level ; z=1.96

therefore 95% confidence interval for the proportion =p -/+ z*std error =0.1433 ; 0.1618

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