3. Many people apply for jobs to serve as paramedics or firefighters, yet they c
ID: 3053382 • Letter: 3
Question
3. Many people apply for jobs to serve as paramedics or firefighters, yet they cannot complete basic physical fitness standards. A recent study found that 77% of all candi- dates for paramedic and firefighter positions were overweight or obese (Obesity, March 19, 2009).
a. What is the expected value and the standard deviation of the sample proportion de- rived from a random sample of 100 candidates for paramedic or firefighter positions?
b. What is the expected value and the standard deviation of the sample proportion de- rived from a random sample of 200 candidates for paramedic or firefighter positions?
c. Comment on the value of the standard deviation as the sample size gets larger.
Explanation / Answer
a) here for sample size n=100
expected proportion =p =0.77
standard deviation of the sample proportion =(p*(1-p)/n)1/2 =0.0421
b)
for sample size n=200
expected proportion =p =0.77
standard deviation of the sample proportion =(p*(1-p)/n)1/2 =0.0298
c)we can see from above that as we increase sample size std deviation of sample proportion decreases; whcih validates law of large numbers accoeding to which with increase in sample size sample proportion is more inclinded to be near to population proprtion