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Chapter 11: Q 11.22. (page 460)

In each of Exercises 11.19-11.24, we have given a likely nange for the observed value of a sample proportion p^.

a. Based on the given range, identify the educated guess that should be used for the observed value of 尾^to calculafe the required sample size for a prescribed confidence level and margin of error.

b. Ldentify the observed values of the sample proportion that will yield a larger margin of error than the one specified if the educated guess is used for the sample-size computation.

0.7or greater

Short Answer

Expert verified

Part a) the educated guess is0.7
Part b), the observed values of the sample proportion that will yield larger margin of error is0.3<p^<0.7

Step by step solution

01

Step 1:Given information

0.7or greater

02

Step 2:Explaination Part a)

Identify the educated guess when the range is 0.7or greater.

Educated guess for p^can be identified by which the value in the range is closest to 0.5Here, the value0.7in the range is closest to 0.5Hence, educated guess p^gis 0.7

03

Step 2:Explaination Part b)

Identify the observed values of the sample proportion that will yield larger margin of error.

The observed value of p^had turned out to be larger than 0.3but smaller than 0.7, which provides the larger margin of error. Hence, the observed values of the sample proportion that will yield larger margin of error is0.3<p^<0.7.

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Most popular questions from this chapter

Margin of error =0.01

Confidence level=95%

Educated guess =0.3

(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.

A Wall Street Journal article, titled "Hypertension Drug Linked to Cancer," reported on a study of several types of high-blood-pressure drugs and links to cancer. For one type, called calcium-channel blockers, 27of 202elderly patients taking the drug developed cancer. For another type, called beta-blockers, 28of 424other elderly patients developed cancer. Find a 90%confidence interval for the difference between the cancer rates of elderly people taking calcium-channel blockers and those taking beta-blockers. Note: The results of this study were challenged and questioned by several sources that claimed, for example, that the study was flawed and that several other studies have suggested that calcium-channel blockers are safe.

11.91 Economic Stimulus. In a national poll, 1053 U.S. adults were asked, "As you may know, Congress is considering a new economic stimulus package of at least 800 billion dollars. Do you favor or oppose Congress passing this legislation?" Of those sampled, 548 favored passage.
a. At the 5% significance level, do the data provide sufficient evidence to conclude that a majority (more than 50% ) of U.S. adults favored passage?
b. The headline on the website featuring the survey read, "In U.S., Slim Majority Supports Economic Stimulus Plan." In view of your result from part (a), discuss why the headline might be misleading.
c. How could the headline be made more precise?

11.94 Drowning Deaths. In the article "Drowning Deaths of Zero to Five Year Old Children in Victorian Dams, 1989-2001" (Australian Journal of Rural Health, Vol. 13, Issue 5, pp. 300-308), L. Bugeja and R. Franklin examined drowning deaths of young children in Victorian dams to identify common contributing factors and develop strategies for future prevention. Of 11young children who drowned in Victorian dams located on farms, 5 were girls, At the 5% significance level, do the data provide sufficient evidence to conclude that, of all young children drowning in Victorian dams located on farms, less than half are girls?

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=3

n=100

H0:p=0.04

Ha:p鈮�0.04

伪=0.10
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