Question

A marketing director is considering a new marketing campaign. The latest report from a consumer focus group indicated that 0.86 of customers responded favorably. The marketing director wants to assert with 99% confidence that the margin of error of the estimate will be no more than 0.05 in his budget request report to the CFO. Find the minimum sample size needed.

Answer 1

Solution :

Given that,

= 0.86

1 - = 1 - 0.86 = 0.14

margin of error = E = 0.05

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.58    ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (2.58 / 0.05)2 * 0.86 * 0.14

=320.5

Sample size = 321