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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’s 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’s 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^±Zα/2×p^(1-p^)n

0.63+Zα/2×0.63(1-0.63)100=0.695

Zα/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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Most popular questions from this chapter

A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who think the drinking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: “Do you think that the drinking age should be reduced to eighteen in light of the fact that 18-year-olds are eligible for military service?” He asks listeners to go to his website and vote “Yes” if they agree the drinking age should be lowered and “No” if not. Of the 100 people who voted, 70 answered “Yes.” Which of the following conditions are violated?

I. Random

II. 10%

III. Large Counts

a. I only

b. II only

c. III only

d. I and II only

e. I, II, and III

Catching goldfish for schoolCarly and Maysem plan to be preschool teachers after they graduate from college. To prepare for snack time, they want to know the mean number of goldfish crackers in a bag of original-flavored goldfish. To estimate this value, they randomly selected12 bags of original-flavored goldfish and counted the number of crackers in each bag. Here are their data:

Construct and interpret a 95% confidence interval for the true mean number of crackers in a bag of original- flavored goldfish.

Scientists collect data on the blood cholesterol levels (milligrams per deciliter of blood) of a random sample of 24laboratory rats. A 95%confidence interval for the mean blood cholesterol level μis 80.2to 89.8. Which of the following would cause the most worry about the validity of this interval?

a. There is a clear outlier in the data.

b. A stem plot of the data shows a mild right skew.

c. You do not know the population standard deviation σ.

d. The population distribution is not exactly Normal.

e. None of these are a problem when using a t interval.

Refer to Exercise 55. Suppose that Gallup wanted to cut the margin of error in half from 3percentage points to 1.5percentage points. How should they adjust their sample size?

a. Multiply the sample size by 4.

b. Multiply the sample size by 2.

c. Multiply the sample size by 1/2.

d. Multiply the sample size by 1/4.

e. There is not enough information to answer this question.

Losing weight Refer to Exercise 6.

a. Explain what would happen to the length of the interval if the confidence level was decreased to 90%.

b. How would a 95%confidence interval based on triple the sample size compare to the original 95%interval?

c. As Gallup indicates, the 3percentage point margin of error for this poll includes only sampling variability (what they call “sampling error”). What other potential sources of error (Gallup calls these “non sampling errors”) could affect the accuracy of the 95% confidence interval?
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