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Exam 8: Interval Estimation

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Question 61

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Exhibit 8.4.According to a report in USA Today (February 1,2012) ,more and more parents are helping their young adult children get homes.Suppose 8 persons in a random sample of 40 young adults who recently purchased a home in Kentucky got help from their parents.You have been asked to construct a 95% confidence interval for the population proportion of all young adults in Kentucky who got help from their parents. Refer to Exhibit 8.4.If a 99% confidence interval is constructed instead of a 95% confidence interval for the population proportion,then ____________________.

A) The resulting margin of error will increase and the risk of reporting an incorrect interval will increase
B) The resulting margin of error will decrease and the risk of reporting an incorrect interval will increase
C) The resulting margin of error will increase and the risk of reporting an incorrect interval will decrease
D) The resulting margin of error will decrease and the risk of reporting an incorrect interval will decrease

E) C) and D)
F) B) and C)

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Question 62

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Newscasters wish to predict the outcome of the next presidential election with 99% confidence and a margin of error equal to 0.08.Find the appropriate sample size to accomplish this goal.

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Question 63

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How is the unbiasness of estimators defined?

Exhibit 8-6.A sample of 1400 American households was asked if they planned to buy a new car next year.Of the respondents,34% indicated they planned to buy a new car next year. Refer to Exhibit 8-6.Construct a 90% confidence interval of the proportion of American households who expect to buy a new car next year.

The Department of Education wishes to estimate average SAT score among U.S.high school students.How many students would they have to sample,given that the test has a known population standard deviation of 100,in order to ensure that the margin of error was no more than 20 for a 99% confidence interval?

Given a sample mean of 27 and a sample standard deviation of 3.5 computed from a sample of size 36,find a 95% confidence interval on the population mean.

A researcher in campaign finance law wants to estimate the proportion of elementary,middle,and high school teachers who contributed to a candidate during a recent election cycle.Given that no prior estimate of the population proportion is available,what is the minimum sample size such that the margin of error is no more than 0.03 for a 95% confidence interval?

In an examination of purchasing patterns of shoppers,a sample of 16 shoppers revealed that they spent,on average,$54 per hour of shopping.Based on previous years,the population standard deviation is thought to be $21 per hour of shopping.Assuming that the amount spent per hour of shopping is normally distributed,find a 90% confidence interval for the mean amount.

Find the minimum sample size when we want to construct a 90% confidence interval on the population proportion for the support of candidate A in the following mayoral election.Candidate A is facing two opposing candidates.In a preselected poll of 100 residents,22 supported her.The desired margin of error is 0.08.

Suppose taxi fare from Logan Airport to downtown Boston is known to be normally distributed with a standard deviation of $2.50.The last seven times John has taken a taxi from Logan to downtown Boston the fares have been $22.10,$23.25,$21.35,$24.50,$21.90,$20.75,and $22.65.What is a 95% confidence interval for the population mean taxi fare?

Which of the following is a point estimate?