Exam 17: Additional Topics in Sampling

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: An auditor,examining a total of 800 accounts receivable by a corporation,selected a random sample of 60 accounts.The sample mean is $130.54 and the sample standard deviation is $42.56. -Using an unbiased estimation procedure,find an estimate of the variance of the sample mean.

Proportional allocation occurs when the proportion of sample members from any stratum is the same as the proportion of population members in that stratum.

Explain in detail what is meant by "cluster sampling has a superficial resemblance to stratified sampling."

The distinction between cluster sampling and stratified sampling is that in the former a random sample of clusters is taken,while in the latter a complete census of stratum members is drawn.

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. -If a total sample of 120 students is taken,determine the number of freshmen and sophomores under the proportional allocation scheme.

A sales representative has 798 accounts.She wants to take a random sample to determine the mean amount of yearly sales for these accounts.From past research,she knows that the population standard deviation is approximately $37,000.How large a sample should she take in order to estimate the population mean within $10,000 at a 99% level of confidence?

An unbiased estimator of the variance of the estimator of μ follows from the fact that the samples in each stratum are independent of one another.

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. -Compare and contrast stratified sampling and cluster sampling.Under what circumstances would these techniques be chosen over a simple random sample?

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 stratified sampling and state its advantages.

In order to take a simple random sample from each stratum,each individual member of the population must be identifiable as belonging to one,and only one,of the strata.

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. -For a sample of 126 observations from a population of 873,the sample mean is 17.2 and the sample standard deviation is 2.4.Create a 99% confidence interval for the population mean.

In stratified random sampling,it is necessary to take the same number of sample members from every stratum.

An unbiased estimation procedure for the variance of the estimator of the overall population mean yields the point estimate = .

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: An auditor,examining a total of 800 accounts receivable by a corporation,selected a random sample of 60 accounts.The sample mean is $130.54 and the sample standard deviation is $42.56. -A statistician observed,for the population mean,a confidence interval running from $119.42 to $135.42.What is the probability of this interval? What is α?

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. -If a total sample of 120 students is taken,determine the number of freshmen and sophomores under the optimum allocation scheme,assuming that the stratum population standard deviations are the same as the corresponding sample values.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A chemistry class at a university in the Midwest has 450 students.The final examination is optional - it can raise,but not lower,a student's grade.Of a random sample of 100 students,40 indicated that they would take the final examination. -Find a 90% confidence interval for the total number of students intending to take the final examination.

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 mean monthly expenditures.

In which of the following sampling methods are the individuals of a population subdivided into mutually exclusive and collectively exhaustive separate subpopulations with a common characteristic?

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. -If a total sample of 120 students is taken,determine the number of juniors and seniors under the proportional allocation scheme.

From the unbiased estimation procedure for the variance of the stratum sample mean,the point estimate is given by = ×