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Chapter 8: Q 51. (page 523)

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. What sample size is required to obtain a 90%confidence interval with a margin of error of at most 0.04?

Short Answer

Expert verified

Sample size is423.

Step by step solution

01

Given Information

Confidence Level =90%

E=0.04

Corresponding to 90%confidence level role="math" localid="1654454884514" Zα2=1.645

02

Calculation of Sample Size

The formula used is:

n=p^(1-p^)za2E2

Regarding p^, no detail is given assume it as 0.50

Hence, n=p^(1-p^)za2E2

=0.50(1-0.50)1.6450.042

=422.816≈423

Sample Size is423

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Most popular questions from this chapter

Selling online According to a recent Pew Research Center report, many

American adults have made money by selling something online. In a random sample of 4579American adults, 914reported that they earned money by selling something online in the previous year. Assume the conditions for inference are met.

Determine the critical value z* for a 98% confidence interval for a proportion.

b. Construct a 98% confidence interval for the proportion of all American adults who

would report having earned money by selling something online in the previous year.

c. Interpret the interval from part (b).

Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first year at a major university. The interval is to have a margin of error of at most \(2. Based on last year’s book sales, we estimate that the standard deviation of the amount spent will be close to \)30. The number of observations required is closest to which of the following?

a. 25

b.30

c. 225

d. 609

e. 865

It’s about ME Explain how each of the following would affect the margin of error of a confidence interval, if all other things remained the same.

a. Increasing the confidence level

b. Quadrupling the sample size

More prayer in school Refer to Exercise 5. Interpret the confidence level.

Losing weight A Gallup poll asked a random sample of U.S. adults, “Would you like to lose weight?” Based on this poll, the 95%confidence interval for the population

proportion who want to lose weight is (0.56,0.62).

a. Interpret the confidence interval.

b. What is the point estimate that was used to create the interval? What is the margin of error?

c. Based on this poll, Gallup claims that more than half of U.S. adults want to lose weight. Use the confidence interval to evaluate this claim.
See all solutions

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