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Chapter 11: Q. 11.43 (page 460)

Obtain a sample size

Margin of error =0.01

Confidence level =95%

likely range=0.2-0.4

Short Answer

Expert verified

The required sample size is9,604.

Step by step solution

01

Given information

Margin of error =0.01

Confidence level =95%

Likely range 0.2-0.4

02

Explanation

From the given data

When the margin of error is 0.01and the confidence level is 95%, calculate the sample size.

With a 95%confidence level, the required value of za2from table areas under the standard normal curve is 1.96

Use pg'=0.4because the value in the range closet to 0.5

The sample size is

n=0.25z伪炉EE2

=0.251.960.012

=0.25(38,416)

=9,604.

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Most popular questions from this chapter

11.99 Of the quantities p1,p2,x1,x2,p^1,p^2, and p^p.
a. which represent parameters and which represent statistics?
b. which are fixed numbers and which are variables?

In discussing the sample size required for obtaining a confidence interval with a prescribed confidence level and margin of error, we made the following statement: "If we have in mind a likely range for the observed value of p^, then, in light of Fig. 11.1, we should take as our educated guess for p^the value in the range closest to 0.5"Explain why.

a. Determine the sample proportion.

b. Decide whether using the one-proportion z-test is appropriate.

c. If appropriate, use the one-proportion z-test to perform the specified hypothesis test.

x=35

n=50

H0:p=0.6

role="math" localid="1651304589496" Ha:p>0.6

伪=0.05

Refer to the study on ordering vegetarian considered in Examples 11.8-11.10.

a. Without making a guess for the observed values of the sample proportions, find the common sample size that will ensure a margin of error of at most 0.01for a 90%confidence interval. Hint: Use Exercise 11.133.

b. Find a90%confidence interval for p1-p2if, for samples of the size determined in part (a), 38.3%of the men and 43.7%of the women sometimes order veg.

c. Determine the margin of error for the estimate in part (b), and compare it to the required margin of error specified in part (a).

Since 1973, Gallup has asked Americans how much confidence they have in a variety of U.S. institutions. One question asked of those polled is whether they have a great deal of confidence in banks. In 2007, of a random sample of 1008adult Americans, 413said yes; and, in 2013, of a random sample of 1529adult Americans, 398said yes. For the two years, find and interpret a95% confidence interval for the difference between the percentages of adult Americans who had a great deal of confidence in banks.
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