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 80​% confident that his estimate is within seven percentage points of the true population​ percentage

Answer 1

Solution :

Given that,

= 0.5 ( asume 0.5)

1 - = 1 - 0.5= 0.5

margin of error = E = 7% = 0.07

At 80% confidence level the z is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.10

Z/2 = Z0.10 = 1.28 ( Using z table )

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

= (1.28 / 0.07)2 * 0.5 * 0.5

= 83.59

Sample size =84