Exam 8: Interval Estimation

An estimator is unbiased if its expected value equals the estimated population parameter.

How does an interval estimator differ from a point estimator?

Suppose we wish to find the required sample size to find a 90% confidence interval for the population proportion with the desired margin of error.If there is no rough estimate of the population proportion,what value should be assumed for ?

Exhibit 8-5.A sample of 2,007 American adults was asked how they viewed China,with 17% of respondents indicating "unfriendly" and 6% of respondents indicating "an enemy" (Gallup,Nov.30 - Dec.18,2011). Refer to Exhibit 8-5.Construct a 95% confidence interval of the proportion of American adults who view China as either "unfriendly" or as "an enemy."

Confidence intervals of the population mean may be created for the cases when the population standard deviation is known or unknown.How are these two cases treated differently?

An estimator is consistent if it approaches the estimated population parameter as the sample size grows larger.

According to a report in USA Today (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 got 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?

A basketball coach wants to know how many free throws an NBA player shoots during the course of an average practice.The coach takes a random sample of 43 players and finds the average number of free throws shot per practice was 225 with a standard deviation of 35.Construct a 99% confidence interval for the average number of free throws in practice.

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 98% confidence interval of the proportion of American households who expect to buy a new car next year.

A large city recently surveyed 1,354 street lights,finding that 4.2% of them had burned out.Construct a 99% confidence interval for the proportion of the city's street lights that are burned out.

Exhibit 8-2.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. Refer to Exhibit 8-2.Construct a 90% confidence interval for the mean duration of the foreclosure process in Boston.

An unbiased estimator is efficient if its standard error is higher than that of other unbiased estimators of the estimated population parameter.

At a particular 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.

Exhibit 8-2.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. Refer to Exhibit 8-2.Construct a 99% confidence interval for the mean duration of the foreclosure process in Boston.

A large earthquake hit a city in South America.A survey of 2,000 houses found that 600 of them had collapsed.Construct a 95% confidence interval for the proportion of collapsed houses.

A sample of the weights of 35 babies is taken from the local hospital maternity ward.The point estimate for the mean weight of the babies is 110.2 ounces with a sample standard deviation of 23.4 ounces.Construct a 90% confidence interval for the population mean baby weight at this hospital.Interpret this interval.

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

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.

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.In order 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 above interval?

The GPA of accounting students in a university is known to be normally distributed.A random sample of 20 accounting students results in a mean of 2.92 and a standard deviation of 0.16.Construct the 95% confidence interval for the mean GPA of all accounting students at this university.