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Chapter 8: Q 5. (page 506)

Prayer in school A New York Times/CBS News Poll asked a random sample of U.S. adults the question 鈥淒o you favor an amendment to the Constitution that would permit organized prayer in public schools?鈥� Based on this poll, the 95%confidence interval for the population proportion who favor such an amendment is (0.63,0.69).

a. Interpret the confidence interval.

b. What is the point estimate that was used to create the interval? What is the margin of error?

c. Based on this poll, a reporter claims that more than two-thirds of U.S. adults favor such an amendment. Use the confidence interval to evaluate this claim.

Short Answer

Expert verified

a. 95%confidence interval for the population is given by (0.63,0.69)

b. The margin of error is 0.03

c. There is no evidence that 0.67US Adults favour amendment.

Step by step solution

01

Given Information

Confidence Interval is 95%

Population proportion is0.63,0.69

02

Concept Used

Formulas p^=UCL+LCL2

ME=UCL-LCL2

03

a. Interpreting Confidence Level

It refers to 95%assurance that population proportion who favor such an amendment is 0.63,0.69.

Others do not favour amendment do not come in this range.

04

b. Point Estimate and Margin of Error

Proportion is p^=0.63+0.692

and Margin of Error ME=0.69-0.632=0.03

Point Estimate: Since it lies halfway of confidence interval, point estimate is average of boundaries of interval. Here point estimate of 0.63,0.69is 0.66

Margin of Error: It is half the difference of confidence interval.

05

c. Evaluating the Claim

From the data and above calculations, it is observed that confidence interval contains 23=0.66.

It means 0.67of US adults favours amendment.

Hence, it is not a convincing evidence.

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