Exam 8: Estimating Single Population Parameters

For a given sample size and a given confidence level,the closer π is to 1.0,the greater the margin of error will be.

Recently,a marketing research company reported that based on a random sample of 300 households the mean number of trips to a major shopping mall per month per household is 4.12 trips.This value is referred to as a parameter and is subject to sampling error.

Suppose that an internal report submitted to the managers at a bank in Boston showed that with 95 percent confidence,the proportion of the bank's customers who also have accounts at one or more other banks is between .45 and .51.Given this information,what sample size was used to arrive at this estimate?

When σ is unknown,one should use an estimate that is considered to be at least as large as the true σ.This will provide a conservative sample size to be on the safe side.

A Parks and Recreation official surveyed 200 people at random who have used one of the city's parks.The survey revealed that 26 resided outside the city limits.If she had to arrive at one single value to estimate the true proportion of park users who are residents of the city it would be 0.13.

A study was recently conducted to estimate the mean cholesterol for adult males over the age of 55 years.The following random sample data were observed: Given this information,what is the point estimate for the population mean?

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: = $88.60 s = $30.79 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?

A financial analyst is interested in estimating the proportion of publicly traded companies on the New York Stock Exchange that have cash balances that are more than 10 percent of the total assets of the company.A random sample of n = 100 companies shows that 13 had cash balances of more than 10 percent of assets.Based on this information,develop and interpret a 90 percent confidence interval estimate for the population proportion.

A traffic engineer plans to estimate the average number of cars that pass through an intersection each day.Based on previous studies the standard deviation is believed to be 52 cars.She wants to estimate the mean to within ± 10 cars with 90 percent confidence.The needed sample size for n is:

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.

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.Based on a 95 percent confidence level,the upper and lower confidence interval limits are approximately 0.3525 to 0.5475.

Chicago Connection,a local pizza company,delivers pizzas for free within the market area.The delivery drivers are paid $2.00 per delivery plus they get to keep any tips.To estimate the proportion of deliveries that result in a tip to the driver,a random sample of 64 deliveries was selected.Of these,48 times a tip was received.Based on this information,and using a 95 percent confidence level,the upper limit for the confidence interval estimate is about .1061.

In a situation where we know the population standard deviation but wish to estimate the population mean using a 90 percent confidence interval,the critical value is z = ±1.645.

If a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean,she can:

The manager in charge of concessions at an NFL football stadium is interested in estimating the mean dollars that are spent per person attending the games.A pilot sample of n = 50 people has revealed a sample mean and standard deviation of $12.35 and $2.35 respectively.He wishes to estimate the population mean within ± $0.20 of the true mean and wishes to have a confidence level of 95 percent.Given this,he needs to sample an additional 481 people.

A publisher is interested in estimating the proportion of textbooks that students resell at the end of the semester.He is interested in making this estimate using a confidence level of 95 percent and a margin of error of ± 0.02.Based upon his prior experience,he believes that π is somewhere around 0.60.Given this information,the required sample size is over 2,300 students.

The purpose of a pilot sample is:

The sampling distribution for a proportion has a formula for that standard error that involves using π.Yet when a confidence interval is calculated for a proportion,the standard error formula uses the sample proportion.Why do they differ?

Which of the following will increase the width of a confidence interval (assuming that everything else remains constant)?

Chicago Connection,a local pizza company,delivers pizzas for free within the market area.The delivery drivers are paid $2.00 per delivery plus they get to keep any tips.To estimate the proportion of deliveries that result in a tip to the driver,a random sample of 64 deliveries was selected.Of these,48 times a tip was received.Based on this information,and using a 95 percent confidence level,the margin of error for the estimate is approximately ± .1061.