Exam 17: Additional Topics in Sampling

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The faculty advisor at a local business school is interested in determining the monthly expenditures on stationeries for students.The advisor samples some students from each class and computes the sample mean and standard deviation for each class. -Find a 98% confidence interval for the total expenditures.

If stratified random sampling is employed,the pilot study can be used to provide estimates of the individual stratum variances.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A supermarket chain has 25 stores in the North,30 in the South,50 in the Midwest,and 35 in the West.Using a proportional allocation of a random sample of 30% of the outlets,the manager records the following means and standard deviations. -Find a 95% confidence interval for the total sales.

For a sample of 145 observations from a population of 744,the sample mean is 22.6 and the sample standard deviation is 3.8.Create a 90% confidence interval for the population mean.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The mean household income,in dollars,must be estimated for a town that is divided into three districts.The relevant information is shown in the table. A 95% confidence interval for the population mean that extends $550 on each side of the sample estimate is required. -Determine how many sample observations are needed under the optimal allocation scheme.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In a stratified random sample of students on a campus,sample members were asked to rate,on a scale of 1 (poor)to 5 (excellent),opportunities for improving the college infrastructure.The results are shown in the table below. -If a total sample of 150 students is taken,determine the number of freshmen and sophomores under the proportional allocation scheme.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A sales representative has 425 accounts.From a random sample of 60 of these accounts,she found that the average yearly order was $1,250 with a standard deviation of $70.She also found that 28 out of 60 in the sample have placed an order in the last four weeks. -Find a 90% confidence interval for the total amount of sales for the sales representative.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: An auditor is faced with reviewing 1,098 invoices.From a random sample of 134 of these accounts,he found that the average amount was $548 with a standard deviation of $129.He also found that 42 out of the 134 in the sample were from out-of-state suppliers. -Find a 95% confidence interval for the proportion of all invoices that are from out-of-state suppliers.

An apartment complex manager randomly selects 10 buildings from the complex's 30 buildings,and then interviews one household member from each apartment in the 10 buildings.This is an example of cluster sampling.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The faculty advisor for the marketing society at a local business school is interested in determining the monthly expenditures on entertainment for marketing students.The advisor samples some students from each class and computes the sample mean and standard deviation for each class. -Find a 90% confidence interval for the total expenditures.

A stratified sampling technique is used when the population can conveniently be subdivided into relatively small and geographically compact units.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A sales representative has 425 accounts.From a random sample of 60 of these accounts,she found that the average yearly order was $1,250 with a standard deviation of $70.She also found that 28 out of 60 in the sample have placed an order in the last four weeks. -Estimate the proportion of all accounts that placed an order within the last four weeks.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The faculty advisor for the finance society at a local business school is interested in determining the proportion of finance students going on a field trip.The advisor samples some students from each class and computes the sample proportion for each class. -The alumni association for MBA students at a local university has 1,532 active members.Suppose you are interested in determining the average number of hours alumni spend in volunteer work each month.You know from past experience that the population standard deviation is approximately 7.2 hours.How large a sample would you need to ensure that the sample mean is within 3 hours with a 95% confidence level?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The U.S.Senate has 100 members.62 senators' offices obtained certain information from the individuals responsible for managing correspondence.Of these,40 specified a minimum number of letters that must be received on an issue before a form letter in response is created. -Explain cluster sampling and state its advantages.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: An auditor is faced with reviewing 1,098 invoices.From a random sample of 134 of these accounts,he found that the average amount was $548 with a standard deviation of $129.He also found that 42 out of the 134 in the sample were from out-of-state suppliers. -Estimate the proportion of all invoices that are from out-of-state suppliers.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: An auditor is faced with reviewing 1,098 invoices.From a random sample of 134 of these accounts,he found that the average amount was $548 with a standard deviation of $129.He also found that 42 out of the 134 in the sample were from out-of-state suppliers. -Find a 95% confidence interval for the total dollar value of these invoices.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A sales representative has 425 accounts.From a random sample of 60 of these accounts,she found that the average yearly order was $1,250 with a standard deviation of $70.She also found that 28 out of 60 in the sample have placed an order in the last four weeks. -A simple random sample of 250 from a total 1,200 colleges in the United States contains 40 colleges that charge a technology fee in addition to the tuition fee.Find a 99% confidence interval for the proportion of all colleges charging a technology fee.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In a stratified random sample of students on a small campus,sample members were asked to rate,on a scale of 1 (poor)to 5 (excellent),opportunities for extracurricular activities.The results are shown in the table below. -Find a 95% confidence interval for the mean rating given by all juniors and seniors on the campus.

In many practical applications,nonprobabilistic methods are used for selecting sample members,primarily as a matter of convenience.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The faculty advisor for the finance society at a local business school is interested in determining the proportion of finance students going on a field trip.The advisor samples some students from each class and computes the sample proportion for each class. -A simple random sample of 400 from a total 1,400 colleges in the United States contains 45 colleges that charge a technology fee in addition to the tuition fee.Find a 95% confidence interval for the proportion of all colleges charging a technology fee.