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Exam 8: Interval Estimation

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Question 51

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What conditions are required by the central limit theorem before a confidence interval of the population mean may be created?

A) The underlying population must be normally distributed.
B) The underlying population must be normally distributed if the sample size is 30 or more.
C) The underlying population need not be normally distributed if the sample size is 30 or more.
D) The underlying population need not be normally distributed if the population standard deviation is known.

E) All of the above
F) B) and D)

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Question 52

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What is for a 90% confidence interval of the population mean?

A) 0.48
B) 0.49
C) 1.645
D) 1.96

E) None of the above
F) All of the above

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Question 53

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According to a report in USAToday (February 1,2012) ,more and more parents are helping their young adult children buy homes.You would like to construct a 90% confidence interval of the proportion of all young adults in Louisville,Kentucky,who received help from their parents in buying a home.How large a sample should you take so that the margin of error is no more than 0.06?

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?

When the required sample size calculated by using a formula is not a whole number,what is the best choice for the required sample size?

A string quartet in Maui wants to better understand its income stream,which primarily comes from playing at weddings.The cellist records the number of weddings the quartet plays in six successive months.Construct a 90% confidence interval from her results: 3,5,7,4,4,and 5.

Professors of accountancy are in high demand at American universities.A random sample of 28 new accounting professors found the average salary was $135 thousand with a standard deviation of $16 thousand.Assume the distribution is normally distributed.Construct a 90% confidence interval for the salary of new accounting professors.Answers are in thousands of dollars.

Statisticians like precision in their interval estimates.A low margin of error is needed to achieve this.Which of the following supports this when selecting sample sizes?

The parameter p represents the ________ of successes in the population.

The average natural gas bill for a random sample of 21 homes in 19810 zip code during the month of March was $311.90 with a sample standard deviation of $51.60.The 90% confidence interval around this sample mean is _______.

A company manager thinks he is overpaying for fertilizer at $174 per ton.To find out,he collects fertilizer prices per ton from five distributors.Construct a 90% confidence interval from his results: 128,140,170,166,and 156.

At a particular academically challenging high school,the average GPA of a high school senior is known to be normally distributed.After a sample of 20 seniors is taken,the average GPA is found to be 2.71 and the variance is determined to be 0.25.Find a 90% confidence interval for the population mean GPA.

Each portion of the SAT exam is designed to be normally distributed such that it has a population standard deviation of 100 and a mean of 500.However,the mean has changed over the years as less selective schools began requiring the SAT,and because students later began to prepare more specifically for the exam.Construct a 90% confidence interval for the population mean from the following eight scores from the math portion,using the population standard deviation of 100: 450,660,760,540,420,430,640,and 580.

The Department of Education wishes to estimate the 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?

For a given confidence level and sample size,which of the following is true in the interval estimation of the population mean when σ is known?

Pure-bred dogs competing in shows must often meet specific height criteria to be within the breed standard.A new breed of dog,the pug-cock-a-poo,has been approved by a kennel club.To establish the breed standard,the organization of breeders has taken the height from a sample of 25 pug-cock-a-poos and found the sample mean to equal 14 inches.The variance of this sample is 2.25.a.Construct a 90% confidence interval for the population mean height of the pug-cock-a-poos.b.What assumption is necessary for constructing the aforementioned interval?

The ___________ determine the extent of the broadness of the tails of the distribution.

For a given confidence level and sample size n,the width of the confidence interval for the population mean is narrower,the greater the population standard deviation σ.

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.

The t_df distribution is similar to the z distribution because ___________________________________________.