Question

An automobile insurance company wants to determine from a sample, what proportion of its thousands of policyholders intend to buy a new car within the next twelve months. Assume a 95 percent level of confidence. A committee within the company estimates that the proportion of policyholders planning to buy a new car in the next twelve months is 0.7.  How large a sample is needed if the company wants to be within 0.03 of the true proportion?  How large a sample is needed if the company wants to be within 0.03 of the true population, but no estimate is available?

Answer 1

Solution :

Given that,

(a)

= 0.7

1 - = 0.3

margin of error = E = 0.03

Z_/2 = 1.96

sample size = n = (Z _{/ 2} / E)² * * (1 - )

= (1.96 / 0.03)² * 0.7 * 0.3

= 897

sample size = n = 897

(b)

= 0.5

1 - = 0.5

sample size = n = (Z _{/ 2} / E)² * * (1 - )

= (1.96 / 0.03)² * 0.5 * 0.5

= 1068

sample size = n = 1068