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The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .30. a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02? Use 95% confidence. b. Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population? c. What is the 95% confidence interval for the proportion of smokers in the population?

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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BuyFindarrow_forward

STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 8, Problem 57SE
Textbook Problem
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The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .30.

  1. a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02? Use 95% confidence.
  2. b. Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population?
  3. c. What is the 95% confidence interval for the proportion of smokers in the population?

a.

To determine

Find sample size that is used to estimate the proportion of smokers in the population if the margin of error is 0.02 at 95% confidence.

Explanation of Solution

Calculation:

The percentage of the people who smoke under 18 years of age is 0.30 proportion reports given by centers for disease control.

The formula for sample size for an interval estimate of a population proportion is,

n=(zα2)2p(1p)E2 .

The value of p is 0.30.

From the “Table 8.1 value of zα2”, the value of zα2 for 95% is 1

b.

To determine

Find the point estimate of the proportion of population for smokers.

c.

To determine

Find the 95% confidence interval for proportion of smokers in the population.

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Chapter 8 Solutions

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