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Chapter 11: Q. 11.36 (page 460)

Obtain a sample size that will ensure a margin of error of at most the one specified.

Margin of error=0.04

Confidence level=99%

Short Answer

Expert verified

The required sample size is1,037.

Step by step solution

01

Given information

The given data is

Margin of error =0.04

Confidence level =99%

02

Explanation

Margin of error=0.04

Confidence level =99%

When the margin of error is 0.04and the confidence level is 99%, calculate the sample size.

With a 99%confidence level, the required value of za2from table areas under the standard normal curve is 2.575.

The sample size is

n=0.25zα2E2

=0.252.5750.042

=0.25(4,144.14)

=1,036.04

≈1037.

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Most popular questions from this chapter

Margin of error=0.02

Confidence level=90%

Educated guess=0.1

(a) Obtain a sample size that will ensure a margin of error of at most the one specified (provided of course that the observed value of the sample proportion is further from 0.5that of the educated guess.

(b). Compare your answer to the corresponding one and explain the reason for the difference, if any.

Buckling Up. The National Highway Traffic Safety Administration collects data on seat-belt use and publishes results in the document Occupant Restraint Use. Of 1000 drivers 16-24 years old, 79% said that they buckle up, whereas 924 of 1100 drivers 25-69 years old said that they did. At the 1%significance level, do the data provide sufficient evidence to conclude that there is a difference in seat-belt use between the two age groups?

Ballistic Fingerprinting. Refer to Exercise 11.110 and find and interpret a 98%confidence interval for the difference between the percentages of women and men who favor ballistic fingerprinting.

Vasectomies and Prostate Cancer. In the United States, approximately 450,000 vasectomies are performed each year. In this surgical procedure for contraception, the tube carrying sperm from the testicles is cut and tied. Several studies have been conducted to analyze the relationship between vasectomies and prostate cancer. The results of one such study by E. Giovannucci et al. appeared in the paper "A Retrospective Cohort Study of Vasectomy and Prostate Cancer in U.S. Men" (Journal of the American Medical Association. Vol. 269(7), Pp. 878-882), Of 21,300 men who had not had a vasectomy, 69 were found to have prostate cancer; of 22,000 men who had had a vasectomy, 113 were found to have prostate cancer.

a. At the 1% significance level, do the data provide sufficient evidence to conclude that men who have had a vasectomy are at greater risk of having prostate cancer? Consider men who had had a vasectomy Population 2.

b. Is this study a designed experiment or an observational study Explain your answer.

c. In view of your answers to parts (a) and (b), could you reasonably conclude that having a vasectomy causes an increased risk of prostate cancer? Explain your answer.

Obtain a sample size that will ensure a margin of error of at most the one specified.

Margin of error=0.01

Confidence level=95%
See all solutions

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