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 seven 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.)

​b) Assume that a recent survey suggests that about 78% of adults have heard of the brand.

n= ​(Round up to the nearest​ integer.)

​c) Given that the required sample size is relatively​ small, could he simply survey the adults at the nearest​ college?

A.​No, a sample of students at the nearest college is a cluster​ sample, not a simple random​ sample, so it is very possible that the results would not be representative of the population of adults.

B. ​No, a sample of students at the nearest college is a convenience​ sample, not a simple random​ sample, so it is very possible that the results would not be representative of the population of adults.

C. ​Yes, a sample of students at the nearest college is a simple random​ sample, so the results should be representative of the population of adults.

D. ​No, a sample of students at the nearest college is a stratified​ sample, not a simple random​ sample, so it is very possible that the results would not be representative of the population of adults.

Answer 1

Sample size = Z2/2 * p ( 1 - p) / E2

a)

When prior estimate for proportion is not specified, p = 0.50

n = 1.64492 * 0.5 * 0.5 / 0.072

= 138.05

n = 139 (Rounded up to nearest integer)

b)

n = 1.64492 * 0.78 * ( 1 - 0.78) / 0.072

= 94.75

n = 95 (Rounded up to nearest integer)

c)

No, a sample of students at the nearest college is a convenience​ sample, not a simple random​ sample,

so it is very possible that the results would not be representative of the population of adults.