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Exam 8: Interval Estimation

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Question 41

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The sampling distribution of is based on a normal distribution on samples of any size.

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Question 42

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The height of high school basketball players is known to be normally distributed with a standard deviation of 1.75 inches.In a random sample of eight high school basketball players,the heights (in inches)are recorded as 75,82,68,74,78,70,77,and 76.Construct a 95% confidence interval on the average height of all high school basketball players.

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The confidence inter...

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Question 43

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The mortgage foreclosure crisis that preceded the Great Recession impacted the U.S.economy in many ways,but it also impacted the foreclosure process itself as community activists better learned how to delay foreclosure,and lenders became more wary of filing faulty documentation.Suppose the duration of the eight most recent foreclosures filed in the city of Boston (from the beginning of foreclosure proceedings to the filing of the foreclosure deed,transferring the property) has been 230 days,420 days,340 days,367 days,295 days,314 days,385 days,and 311 days.Assume the duration is normally distributed.Construct a 99% confidence interval for the mean duration of the foreclosure process in Boston.

Like the z distribution,the t_df distribution is symmetric around 0,bell-shaped,and with tails that approach the horizontal axis and eventually cross it.

A confidence interval provides a value that,with a certain measure of confidence,is the population parameter of interest.

Candidate A is facing two opposing candidates in a mayoral election.In a recent poll of 300 residents,she has garnered 51% support.Construct a 95% confidence interval on the population proportion for the support of candidate A in the following election.

The minimum sample size n required to estimate a population proportion,with 95% confidence and the assumed most conservative = 0.5,was found to be 122.Which of the following is the approximate value of the assumed desired margin of error?

At an academically challenging high school,the average GPA of a high school senior is known to be normally distributed with a variance of 0.25.A sample of 20 seniors is taken and their average GPA is found to be 2.71.Develop a 90% confidence interval for the population mean GPA.

We draw a random sample of size 36 from a population with standard deviation 3.5.If the sample mean is 27,what is a 95% confidence interval for the population mean?

An environmentalist is measuring the number of spotted leopard lizards in central California per acre.The environmentalist surveys six acres and finds signs of 24,26,30,27,28,and 27 lizards per acre.Construct a 95% confidence interval for the average number of leopard lizards per acre.

The ________ coefficient is equal to 1- α .

A website advertises job openings on its website,but job seekers have to pay to access the list of job openings.The website recently completed a survey to estimate the number of days it takes to find a new job using its service.It took the last 30 customers an average of 60 days to find a job.Assume the population standard deviation is 10 days.Calculate a 95% confidence interval of the population mean number of days it takes to find a job.

A company that produces computers recently tested the battery in its latest laptop in six separate trials.The battery lasted 8.23,7.89,8.14,8.25,8.30,and 7.95 hours before burning out in each of the tests.Assuming the battery duration is normally distributed,construct a 95% confidence interval for the mean battery life in the new model.

According to a report in USAToday (February 1,2012) ,more and more parents are helping their young adult children get homes.Suppose eight persons in a random sample of 40 young adults who recently purchased a home in Kentucky received 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 received help from their parents.If a 99% confidence interval is constructed instead of a 95% confidence interval for the population proportion,then ________________________________________________________________.

A sample of 2,007 American adults was asked how they viewed China,with 17% of respondents calling the country "unfriendly" and 6% of respondents indicating the country was "an enemy".Construct a 99% confidence interval of the proportion of American adults who viewed China as "an enemy."

Bob's average golf score at his local course is 93.6 from a random sample of 34 rounds of golf.Assume that the population standard deviation for his golf score is 4.2.The 90% confidence interval around this sample mean is ______.

A medical engineering company creates x-ray machines.The machines the company sold in 1995 were expected to last six years before breaking.To test how long the machines actually lasted,the company took a simple random sample of six machines.The company got the following results (in years)for how long the x-ray machines lasted: 8,6,7,9,5,and 7.Assume the distribution of the longevity of x-ray machines is normally distributed.Construct a 98% confidence interval for the average longevity of x-ray machines.

The National Center for Education would like to estimate the proportion of students who defaulted on their student loans for the state of Arizona.The total sample size needed to construct a 95% confidence interval for the proportion of student loans in default with a margin of error equal to 4% is ______.

A financial analyst would like to construct a 95% confidence interval for the mean earnings of a company.The company's earnings have a standard deviation of $12 million.What is the minimum sample size required by the analyst if he wants to restrict the margin of error to $2 million?

A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy in a sample of 36 cereal boxes,the sample mean filling weight is calculated as 1.22 pounds.The population standard deviation is known to be 0,06 pounds.Find the 95% confidence interval for the mean.