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 6 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=

b. Assume that a recent survey suggests that about 79% has heard about the brand.

n=

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E =6% = 0.06

At 90% confidence level z

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.65 ( Using z table

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

= (1.65 / 0.06)2 * 0.5 * 0.5

=189

Sample size = 189

b.

Solution :

Given that,

= 79%=0.79

1 - = 1 - 0.79 = 0.21

margin of error = E =6% = 0.06

At 90% confidence level z

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.65 ( Using z table

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

= (1.65 / 0.06)2 * 0.79* 0.21

=125.46

Sample size = 126 rounded