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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% con铿乨ence 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% con铿乨ence 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.

z伪/2=1.645

Sample proportion p鈭�is70%

Convert 70%into decimal.

70100=0.70

Calculate the sample size. Use the formula n=[z伪/2]2p^(1鈭�p^)E2

n=[z伪/2]2p^(1鈭�p^)E2

n=1.6452脳0.70脳(1鈭�0.70)0.042

=356

Hence, the required sample size is356

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Most popular questions from this chapter

Good wood? A lab supply company sells pieces of Douglas fir 4inches long and 1.5inches square for force experiments in science classes. From experience, the strength of these pieces of wood follows a Normal distribution with standard deviation 3000pounds. You want to estimate the mean load needed to pull apart these pieces of wood to within 1000pounds with 95%confidence. How large a sample is needed? Show your work.

- Understand how the margin of error of a confidence interval changes with the sample size and the level of confidence C.

Many television viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Timex Group USA wishes to estimate the proportion of consumers who believe what is shown in Timex television commercials. Let prepresent the true proportion of consumers who believe what is shown in Timex television commercials. What is the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05or less at a 99%confidence level?

(a) 550

(b) 600

(c) 650

(d) 700

(c)750

NAEP scores Refer to Exercise 5. Below your sketch, choose one value of x inside the shaded region and draw its corresponding confidence interval. Do the same for one value of x outside the shaded region. What is the most important difference between these intervals?

A polling organization announces that the proportion of American voters who favor congressional term limits is 64%, with a 95%confidence margin of error of 3%. If the opinion poll had announced the margin of error for 80% confidence rather than 95%confidence, this margin of error would be

(a) 3%, because the same sample is used.

(b) less than 3%, because we require less confidence.

(c) less than 3%, because the sample size is smaller.

(d) greater than 3%, because we require less confidence.

(e) greater than 3%, because the sample size is smaller.

You want to compute a 90%confidence interval for the mean of a population with unknown population standard deviation. The sample size is 30. The value of role="math" localid="1649226392559" tyou would use for this interval is

(a)1.645(b).1.699(c)1.697

(d) 1.96(e) 2.045
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