In a survey of 4356 emergency first responder revealed how o

In a survey of 4,356 emergency first responder revealed how often a responder feels in danger for their life on the job in a given month. 436 said less than 3 times per-month, 729 said 3-5 times per month, 1978 said 6-9 times per month, and 1213 said 10+ times per month. Calculate the population proportion of the number of emergency first responders that said they felt in fear of their life 6-9 times per month, and report the margin of error with 95% confidence.

Solution

the population proportion is = 729/4356 = 16.7 %

then the margin of error with 95% is : (1,96)sqrt[p(1-p)/(n)] = (1.96)sqrt(0.45(1-0.45)/(4356))= +-0.0147

we use p= 1978/4356 =0.45 the largest proportion