Question

The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the brand. How many adults must he survey in order to be 95​% confident that his estimate is within eight percentage points of the true population​ percentage?

​a) Assume that nothing is known about the percentage of adults who have heard of the brand.

n=151

​b) Assume that a recent survey suggests that about 77​% of adults have heard of the brand.

n=?

Answer 1

Solution :

Given that,

a)

= 1 - = 0.5

margin of error = E = 0.08

Z_/2 = 1.96

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

= (1.96 / 0.08)² * 0.5 * 0.5

= 151

sample size = 151

b)

= 0.77

1 - = 1 - 0.77 = 0.23

margin of error = E = 0.08

Z_/2 = 1.96

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

= (1.96 / 0.08)² * 0.77 * 0.23

= 107

sample size = 107