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 95confident that his estimate is within fivepercentage points of the true population​ percentage? Complete parts​ (a) through​ (c) below.​a)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 be90​%confident that his estimate is withinfivepercentage points of the true population​ percentage? Complete parts​ (a) through​ (c) below.​a)Assume that a recent survey suggests that about 80​%of adults have heard of the brand.

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Asked Dec 3, 2019
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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 five
percentage points of the true population​ percentage? Complete parts​ (a) through​ (c) below.
​a)
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
five
percentage points of the true population​ percentage? Complete parts​ (a) through​ (c) below.
​a)Assume that a recent survey suggests that about 80​%of adults have heard of the brand.
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Expert Answer

Step 1

(a)

Given:

Margin of error (E) = 0.05

Confidence level = 95%

Here, sample proportion of the adults is not given. Thus, it is taken as 0.5, that is p̂ = 0.5

Step 2

The critical value of z at 95% confidence level is 1.96.

The...

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Zau/2 xpx(1-p) E n = 1.96 x 0.5x (1-0.5) 0.05 384.16 384 Thus, the number of adults that must be surveyed in order to be 95% confident is 384

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