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 90​% confident that his estimate is within eight percentage points of the true population​ percentage? Complete parts​ (a) through​ (c) below. ​a) Assume that nothing is known about the percentage of adults who have heard of the brand. n = (Round up to the nearest​ integer.)

Answer 1

Solution,

Given that,

=  1 - = 0.5

margin of error = E = 0.08

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05  = 1.645

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

= (1.645 / 0.08 )2 * 0.5 * 0.5

= 105.70

sample size = n = 106