Question

# The brand manager for a brand of toothpaste must plan a campaign designed to increase brand...

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 six 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 79% 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 convenience​ 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 cluster​ sample, not a simple random​ sample, so it is very possible that the results would not be representative of the population of adults.

C. ​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.

D. ​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.

#### Homework Answers

Answer #1

a) At 90% confidence level, the critical value is z0.05 = 1.645

Margin of error = 0.06

or, z0.05 * sqrt(p(1 - p)/n) = 0.06

or, 1.645 * sqrt(0.5(1 - 0.5)/n) = 0.06

or, n = (1.645 * sqrt(0.5 * 0.5)/0.06)^2

or, n = 188

b) Margin of error = 0.06

or, z0.05 * sqrt(p(1 - p)/n) = 0.06

or, 1.645 * sqrt(0.79(1 - 0.79)/n) = 0.06

or, n = (1.645 * sqrt(0.79 * 0.21)/0.06)^2

or, n = 125

c) Option - D) 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.

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