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 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.

Answer #1

a) At 90% confidence level, the critical value is
z_{0.05} = 1.645

Margin of error = 0.06

or, z_{0.05} * 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, z_{0.05} * 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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designed to increase brand recognition. He wants to first determine
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designed to increase brand recognition. He wants to first determine
the percentage of adults who have heard of the brand. How many
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estimate is within eight percentage points of the true population
percentage?
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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 95% confident that his
estimate is within eight percentage points of the true population
percentage?
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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
8080%
confident that his estimate is within
sixsix
percentage points of the true populationpercentage?.
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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?

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
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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 95 confident that his estimate
is within 8 percentage points of the true population percentage?
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