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Chapter 8: Q.46 (page 497)

Starting a nightclub A college student organization wants to start a nightclub for students under the age of 21. To assess support for this proposal, they will select an SRS of students and ask each respondent if he or she would patronize this type of establishment. They expect that about 70% of the student body would respond favorably. What sample size is required to obtain a 90% confidence interval with an approximate margin of error of 0.04? Show your work

Short Answer

Expert verified

From the given information, the required sample size is356.

Step by step solution

01

Given Information

It is given in the question that,

The margin of errorE=0.04

Sample proportionp=70%

Confidence interval =90%

What sample size is required to obtain a 90% confidence interval with an approximate margin of error of 0.04?

02

Step 2: Explanation

The confidence interval is 90%.

Convert 90% into decimal.

90100=0.90

For confidence interval 0.90, use table A.

zα/2=1.645

Sample proportion p∧is70%

Convert 70%into decimal.

70100=0.70

Calculate the sample size. Use the formula n=[zα/2]2p^(1−p^)E2

n=[zα/2]2p^(1−p^)E2

n=1.6452×0.70×(1−0.70)0.042

=356

Hence, the required sample size is356

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