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Chapter 8: Q 58. (page 524)

A newspaper reporter asked an SRS of 100residents in a large city for their opinion about the mayor鈥檚 job performance. Using the results from the sample, the C%confidence interval for the proportion of all residents in the city who approve of the mayor鈥檚 job performance is 0.565to0.695. What is the value of C?

a. 82

b. 86

c. 90

d. 95

e. 99

Short Answer

Expert verified

Option (a) is correct.

Step by step solution

01

Given Information

It is given that n=100

0.565<p<0.695

02

Calculation of Confidence Level

Sample Proportion is calculated as

p^=Lowerlimit+Upperlimit2

p^=0.565+0.6952=0.63

Confidence Interval is given by

p^卤Z伪/2脳p^(1-p^)n

0.63+Z伪/2脳0.63(1-0.63)100=0.695

Z伪/2=0.0650.63(1-0.63)100=1.35

Hence, probability

P(-1.35<Z<1.35)=P(Z<1.35)-P(Z<-1.35)

P(-1.35<Z<1.35)=0.9115-0.0885

P(-1.35<Z<1.35)=0.8230=82.30%=82%

Confidence Level is 82%

Option (a) is correct.

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