Exam 17: Additional Topics in Sampling

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Of the 1400 colleges in the United States,370 have two-year schools and 1030 have four-year schools.In a random sample of 40 two-year schools,it was found that 10 of the schools do not have any faculty holding a Ph.D.degree.In an independent random sample of 60 four-year schools,it was found that only 6 of the schools do not have any faculty holding a Ph.D.degree. -The mean amount of the 800 mortgages taken out in the city of Grand Rapids,Michigan,in the past year must be estimated.Based on previous experience,a real estate broker knows that the population standard deviation is likely to be about $25,000.If a 95% confidence interval for the population mean extends $2,400 on each side of the sample mean,how many sample observations are needed if a simple random sample is taken?

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 total dollar value of these invoices.

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. -Find a 90% confidence interval for the mean rating given by all freshmen and sophomores on the campus.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: An auditor is faced with reviewing 1,294 invoices.From a random sample of 122 of these accounts,she found that the average amount was $639 with a standard deviation of $143.She also found that 37 out of the 122 in the sample were from out-of-state suppliers. -Find a 90% confidence interval for the total dollar value of these invoices.

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. -Estimate the total expenditures for the population.

In cluster sampling,a complete census is taken for each chosen cluster.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A corporation has 30 outlets in the North,40 in the South,60 in the Midwest,and 45 in the West.Using a proportional allocation of a random sample of 20% of the outlets,the manager records the following means and standard deviations. -Find a 99% confidence interval for the population mean.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A sales representative has 398 accounts.From a random sample of 56 of these accounts,she found that the average yearly order was $1,239 with a standard deviation of $73,and that 27 had placed an order within the last 30 days. -Find the 90% confidence interval for the proportion of all accounts that placed an order within the last 30 days.

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. -Find a 95% confidence interval for the proportion of all students going on the field trip.

The drawback of quota sampling is that,since the sample is not chosen using probabilistic methods,there is no valid way of determining the reliability of the resulting estimates.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A corporation has 30 outlets in the North,40 in the South,60 in the Midwest,and 45 in the West.Using a proportional allocation of a random sample of 20% of the outlets,the manager records the following means and standard deviations. -Estimate the total sales for the corporation based on these estimates.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: An auditor is faced with reviewing 1,294 invoices.From a random sample of 122 of these accounts,she found that the average amount was $639 with a standard deviation of $143.She also found that 37 out of the 122 in the sample were from out-of-state suppliers. -Estimate the total dollar value of these invoices.

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. -Estimate the total sales for the corporation based on these estimates.

The actual total sample size required to achieve a particular value for the variance depends on the manner in which the sample observations are allocated among the strata.

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. -Estimate the mean monthly expenditures.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A corporation has 30 outlets in the North,40 in the South,60 in the Midwest,and 45 in the West.Using a proportional allocation of a random sample of 20% of the outlets,the manager records the following means and standard deviations. -Briefly describe what is meant by "two-phase sampling," and discuss its advantages and disadvantages.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A corporation has 30 outlets in the North,40 in the South,60 in the Midwest,and 45 in the West.Using a proportional allocation of a random sample of 20% of the outlets,the manager records the following means and standard deviations. -Estimate the population mean.

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 total amount of sales for the sales representative.

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 the undergraduate students on the campus.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A corporation has 30 outlets in the North,40 in the South,60 in the Midwest,and 45 in the West.Using a proportional allocation of a random sample of 20% of the outlets,the manager records the following means and standard deviations. -A sales representative has 850 accounts.She is interested in determining the proportion of her accounts that have placed an order within the past month.For a standard deviation of 0.5,how large a sample should she take in order to estimate the population proportion within five percent at a 95% level of confidence?