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Chapter 11: Q. 11.33 (page 460)

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

Margin of error=0.02

Confidence level=90%

Short Answer

Expert verified

The required sample size is1692.

Step by step solution

01

Given information

The given data is

Margin of error =0.02

Confidence level =90%

02

Explanation

Margin of error=0.02

Confidence level =90%

When the margin of error is 0.02and the confidence level is 90%, calculate the sample size.

With a 90%confidence level, the required value of za2from table areas under the standard normal curve is 1.645.

The sample size is

n=0.25zα2E2

=0.251.6450.022

=0.25(6,765.0625)

=1,691.266

≈1692.

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Most popular questions from this chapter

Fill in the blanks.

a. The mean of all possible sample proportions is equal to the

b. For large samples, the possible sample proportions have approximately a distribution.

c. A rule of thumb for using a normal distribution to approximate the distribution of all possible sample proportions is that both and are or greater.

Margin of error=0.02

Confidence level=95%

Educated guess=0.6

(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.

x1=18,n1=30,x2=10,n2=20;95%confidence interval

Is College Worth It? In the New York Times article "College Graduates Fare Well in Jobs Market, Even Through Recession," C. Rampell noted that college graduates have suffered through the recession and lackluster recovery with remarkable resilience. Of a random sample of 1020 college graduates, 35 were unemployed; and of a random sample of 1008 high-school graduates (no college), 69 were unemployed.

a. At the 1 T significance level, do the data provide sufficient evidence to conclude that college graduates have a lower unemployment rate than high-school graduates?

b. Find and interpret a98% confidence interval for the difference in unemployment rates of college and high-school graduates.

The Organization for Economic Cooperation and Development (OECD) conducts studies on unemployment rates by country and publishes its findings in the document Main Economic Indicators. Independent random samples of 100and75 people in the civilian labor forces of Finland and Denmark, respectively, revealed 7and 3 unemployed, respectively. Find a 95% confidence interval for the difference between the unemployment rates in Finland and Denmark.
See all solutions

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