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Chapter 11: Q.11.132 (page 478)

Obtain a formula for the margin of error, E, in estimating the difference between two population proportions by referring to Step 2 of Procedure 11.4on page 472 .

Short Answer

Expert verified

The formula of margin of error isE=zα/2p~11-p~1n1+p~21-p~2n2

Step by step solution

01

Given information

Given in the question that, We need to obtain a formula for the margin of error, E in estimating the difference between two population proportions by referring to Step 2 of Procedure 11.4 on page 472 .

02

Explanation

The given values areP1-P2

The formula for the margin of error in estimate the difference between two populations Proportions is,

E=zα/2p~11-p~1n1+p~21-p~2n2

Define the following variables:

n1=The sample size for the first sample.

n2=The sample size for the second sample .

p~1The sample proportion for the first sample.

p~2The sample proportion for the second sample.

Therefore, the formula of margin of error is

E=zα/2p~11-p~1n1+p~21-p~2n2.

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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.

What does the margin of error for the estimate of a population proportion tell you?

Suppose that you are using independent samples to compare two population proportions.

Fill in the blanks.

a. The mean of all possible differences between the two sample proportions equals the

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

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.

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.
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