Question

A marketing researcher for a phone company surveys

165165

people and finds that the proportion of customers who are likely to switch providers when their contract expires is

1717 %.

Complete parts a) and b) below.

a) What is the standard deviation of the sampling distribution of the proportion?

(Round to four decimal places as needed.)

b) If she wants to reduce the standard deviation by half, how large a sample would she need?

(Type a whole number.)

Answer 1

Sol:

sample proportion=p^=0.17

sample szie=n=165

a) What is the standard deviation of the sampling distribution of the proportion?

(Round to four decimal places as needed.)

SD=sqrtp^(1-p^)/n

=sqrt(0.17*(1-0.17)/165)

SD=0.0292

b) If she wants to reduce the standard deviation by half, how large a sample would she need?

0.0146=sqrt(p*1-p)/n

sqauring on both sided

0.000213=0.17*(1-0.17)/n

0.17*(1-0.17)/0.000213=n

n=662.44

n=662

required sample size=662

she needs 662