Exam 8: Estimating Single Population Parameters

A local pizza company is interested in estimating the percentage of customers who would take advantage of a coupon offer.To do this,they give the coupon out to a random sample of 100 customers.Of these,45 actually use the coupon.At the 95 percent confidence level it would be appropriate for the manager to conclude that possibly as many as 50 percent of his customers will redeem the coupon.

Suppose a study of 196 randomly sampled privately insured adults with incomes over 200% of the current poverty level is to be used to measure out-of-pocket medical expenses for prescription drugs for this income class.The sample data are in the file Drug Expenses. Based on the sample data,construct a 95% confidence interval estimate for the mean annual out-of-pocket expenditures on prescription drugs for this income class.Interpret this interval.

An analyst for a financial investment firm recently went through the effort to determine the required sample size for estimating the mean number of transactions per year for the clients of his firm.The calculations,which were based on a 95 percent confidence level and a margin of error of ±3,gave a required sample size of 300.Given this information,the value used for the population standard deviation must have been about 26.5 transactions.

A confidence interval will contain the true population value as long as the point estimate is within the lower to upper limits.

To find a 98 percent confidence interval where the standard deviation is known,the correct z-value to use for the critical value is 2.33.

The margin of error is:

The U.S.Post Office is interested in estimating the mean weight of packages shipped using the overnight service.They plan to sample 300 packages.A pilot sample taken last year showed that the standard deviation in weight was about 0.15 pound.If they are interested in an estimate that has 95 percent confidence,what margin of error can they expect?

An animal shelter wants to estimate the mean number of animals housed daily and they know the standard deviation.If they want to find a 98 percent confidence interval the critical value to use is:

If we are interested in estimating the population mean based on a sample from a population for which we know neither the mean nor the standard deviation,the critical value will be a t value from the t-distribution.

The administrator at Sacred Heart Hospital is interested in estimating the proportion of patients who are satisfied with the meals at the hospital.A random sample of 250 patients was selected and the patients were surveyed.Of these,203 indicated that they were satisfied.Based on this,what is the estimate of the standard error of the sampling distribution?

All other factors held constant,the higher the confidence level,the closer the point estimate for the population mean will be to the true population mean.

In an application to estimate the mean number of miles that downtown employees commute to work roundtrip each day,the following information is given: n = 20 = 4.33 S = 3.50 The point estimate for the true population mean is:

A statement in the newspaper attributed to the leader of a local union stated that the average hourly wage for union members in the region is $13.35.He indicated that this number came from a survey of union members.If an estimate was developed with 95 percent confidence,we can safely conclude that this value is within 95 percent of the true population mean hourly wage.

The State Transportation Department wishes to estimate the mean speed of vehicles on a certain stretch of highway.They wish to estimate the mean within ±0.75 mph and they wish to have a confidence level equal to 99 percent.Based on this information only,they can determine that the required sample size is 320 vehicles.

The Internal Revenue Service (IRS)is interested in estimating the mean amount of money spent on outside tax service by income tax filers filing as single on their individual form.To do this,they have selected a random sample of n = 16 people from this population and surveyed them to determine the sample mean and sample standard deviation.The following information was observed: Given this information,what is the 95 percent confidence interval for the mean dollars spent on outside tax assistance by taxpayers who file as single?

If a manager is interested in estimating the mean time customers spend shopping in a store on each visit to the store,she may want to develop a confidence interval estimate.Suppose,she has determined the required sample size and feels that she cannot afford one that large.What options are available?

A public policy research group is conducting a study of health care plans and would like to estimate the average dollars contributed annually to health savings accounts by participating employees.A pilot study conducted a few months earlier indicated that the standard deviation of annual contributions to such plans was $1,225.The research group wants the study's findings to be within $100 of the true mean with a confidence level of 90%.What sample size is required?

The Hilbert Drug Store owner plans to survey a random sample of his customers with the objective of estimating the mean dollars spent on pharmaceutical products during the past three months.He has assumed that the population standard deviation is known to be $15.50.Given this information,what would be the required sample size to estimate the population mean with 95 percent confidence and a margin of error of ±$2.00?

When σ is unknown,the margin of error is computed by using:

Compute the 90% confidence interval estimate for the population proportion,p,based on a sample size of 100 when the sample proportion, is equal to 0.40.