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Chapter 8: Q 30. (page 522)
High tuition costs Glenn wonders what proportion of the students at his college believe that tuition is too high. He interviews an SRS of of the students and finds of those interviewed think tuition is too high.
All the conditions are met in given case.
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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 confidence interval for the population proportion who favor such an amendment is .
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.
The condition When constructing a confidence interval for a population proportion, we check that the sample size is less than of the population size.
a. Why is it necessary to check this condition?
b. What happens to the capture rate if this condition is violated?
Selling online According to a recent Pew Research Center report, many
American adults have made money by selling something online. In a random sample of American adults, reported that they earned money by selling something online in the previous year. Assume the conditions for inference are met.
Determine the critical value for a confidence interval for a proportion.
b. Construct a confidence interval for the proportion of all American adults who
would report having earned money by selling something online in the previous year.
c. Interpret the interval from part (b).
We love football! A Gallup poll conducted telephone interviews with a random sample of adults aged 18 and older. Data were obtained for 1000 people. Of these, 370 said that football is their favorite sport to watch on television.
a. Define the parameter p in this setting.
b. What point estimator will you use to estimate p? What is the value of the point estimate?
c. Do you believe that the value of the point estimate is equal to the value of p? Explain your answer.
Explaining confidence The admissions director for a university found that is a confidence interval for the mean IQ score of all freshmen. Discuss whether each of the following explanations is correct, based on that information.
a. There is a probability that the interval from role="math" localid="1654200953396" contains .
b. There is a chance that the intervalcontains .
c. This interval was constructed using a method that produces intervals that capture the true mean in of all possible samples.
d. If we take many samples, about of them will contain the interval .
e. The probability that the interval captures is either or , but we don鈥檛 know which.
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