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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 “Do you favor an amendment to the Constitution that would permit organized prayer in public schools?” 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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Most popular questions from this chapter

Power lines and cancer Does living near power lines cause leukemia in

children? The National Cancer Institute spent 5years and $5million gathering data on this question. The researchers compared 638children who had leukemia with 620who did not. They went into the homes and measured the magnetic fields in children’s bedrooms, in other rooms, and at the front door. They recorded facts about power lines near the family home and also near the mother’s residence when she was pregnant. Result: No association between leukemia and exposure to magnetic fields of the kind produced by power lines was found.

a. Was this an observational study or an experiment? Justify your answer.

b. Does this study prove that living near power lines doesn’t cause cancer? Explain your answer.

You want to compute a 90%confidence interval for the mean of a population with an unknown population standard deviation. The sample size is 30. What critical value should you use for this interval?

a. 1.645

b. 1.699

c. 1.697

d. 1.96

e. 2.045

Age and September 11 Refer to Exercise 42. The study also reported that 86% of

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a. Explain why you do not have enough information to give confidence intervals for

millennials and baby boomers separately.

b. Do you think a 95%confidence interval for baby boomers would have a larger or smaller margin of error than the estimate from Exercise 42? Explain your answer.

Gambling and the NCAA Gambling is an issue of great concern to those involved in college athletics. Because of this concern, the National Collegiate Athletic Association (NCAA) surveyed randomly selected student athletes concerning their gambling-related behaviors. Of the 5594Division Imale athletes who responded to the survey, 3547reported participation in some gambling behavior. This includes playing cards, betting on games of skill, buying lottery tickets, betting on sports, and similar activities. A report of this study cited a 1%margin of error.

a. The confidence level was not stated in the report. Use what you have learned to

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b. The study was designed to protect the anonymity of the student athletes who responded. As a result, it was not possible to calculate the number of students who were asked to respond but did not. How does this fact affect the way that you interpret the results?

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d. If the procedure were repeated many times, 95%of the time the population mean systolic blood pressure would be between 122and 138.

e. If the procedure were repeated many times, 95%of the time the sample mean systolic blood pressure would be between 122and138.
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