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A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs? In an actual experiment, 100 consumers were asked to pick the design they preferred. The following data were obtained. Do the data confirm the belief that one design is just as likely to be selected as another? Explain. Design Number of Times Preferred 1 5 2 15 3 30 4 40 5 10

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 4.1, Problem 13E
Textbook Problem
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A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs? In an actual experiment, 100 consumers were asked to pick the design they preferred. The following data were obtained. Do the data confirm the belief that one design is just as likely to be selected as another? Explain.

Design Number of Times Preferred
1 5
2 15
3 30
4 40
5 10

To determine

Compute the probability that assign to each of the experimental outcome. Check whether the data confirm the belief that one design is just as like to another and explain the answer.

Explanation of Solution

Calculation:

Equally likely Outcomes:

The sample points are said to be equally likely if they have equal chance of occurrence.

The experiment contains 5 outcomes and assumes that each outcome is equally likely. Therefore, the probability of each experimental outcome is 15_.

Therefore, if the one design is just as like to be selected by a consumer as any other design then probability that assign to each of the experimental outcome is 0.20(=15).

The probability values for the data is obtained as shown in the table:

DesignFrequencyProbability
155100=0

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Chapter 4 Solutions

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