A marketing researcher for a phone company surveys 200 people and finds that the

Question

A marketing researcher for a phone company surveys 200 people and finds that the proportion of clients who are likely to switch providers when their contract expires is 0.22. a) What is the estimated standard deviation of the sampling distribution of the proportion? b) If she wants to reduce the estimated standard deviation by half, how large of a sample would she need? a) The estimated standard deviation of the sampling distribution of the proportion is. (Round to four decimal places as needed.) b) She will need a sample of (Type a whole number)

Explanation / Answer

here sample size=n=200

and required proportion of clients=p=0.22

here sampling distribution will be binomial distribution with parameter n=200 and p=0.22

variance of proporiton p =p(1-p)/n=0.22*(1-0.22)/200=0.000858

(a) standard deviation =sqrt(variance)=sqrt(0.000858)=0.0293

(b) standard deviation=sd=sqrt(p(1-p)/n)

so sd is directly proportional to 1/sqrt(n) ,

so if we want to reduce the sd by half (1/2) then sample size should be reuired 4 times more i.e. 4*200=800

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