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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=z伪/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=z伪/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=z伪/2p~11-p~1n1+p~21-p~2n2.

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Most popular questions from this chapter

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We have given a likely range for the observed value of a sample proportion p^

0.7orless

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

b. Identify 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.

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: "... we should be aware that, if the observed value of p^is closer to 0.5than is our educated guess, the margin of error will be larger than desired." Explain why.

One-Proportion Plus-Four z-Interval Procedure. To obtain a plus four z-interval for a population proportion, we first add two successes and two failures to our data (hence, the term "plus four") and then apply Procedure 11.1on page 454to the new data. In other words, in place of p^(which is x/n), we use p~=(x+2)/(n+4). Consequently, for a confidence level of 1-伪, the endpoints of the plus-four z-interval are

p~卤za/2路p~(1-p~)/(n+4)

As a rule of thumb, the one-proportion plus-four z-interval procedure should be used only with confidence levels of 90% or greater and sample sizes of 10 or more.
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