3. Many people apply for jobs to serve as paramedics or firefighters, yet they c

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

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