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Chapter 11: Q.11.21 (page 460)

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

0.2orless

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.

Short Answer

Expert verified

(a) The sample proportion is0.2orless

(b) The observed sample proportion values is 0.2<p^<0.8.

Step by step solution

01

Part (a) Step 1: Given Information 

Given in the question that, the confidence interval is 0.2orlesswe have to 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.

02

Part (a) Step 2: Explanation 

The educated guess is the value that is closest to the midpoint of the probable range of 0.2or less.

As a result, the sample proportion is estimated to be 0.2

03

Part (b) Step 1: Given Information 

Given in the question that, the confidence interval is 0.2orlesswe have to

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.

04

Part (b) Step 2: Explanation 

The higher margin of error is found in the value range of 0.2-0.8. As a result, the sample proportion observed values range from0.2-0.8. that is0.2<p^<0.8

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

Margin of error=0.02

Confidence level=90%

Educated guess=0.1

(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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