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. -Estimate the total expenditures for the population.

Which of the following sampling methods would be appropriate when the population can conveniently be subdivided into relatively small and geographically compact units?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: An auditor,examining a total of 650 accounts receivable by a corporation,selected a random sample of 45 accounts.The sample mean is $108.34 and the sample standard deviation is $30.85. -Find a 95% confidence interval for the total amount of the 800 accounts receivable.

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. -A college has 3,400 undergraduate students and 600 graduate students.Researchers are interested in the amount of money spent in a year on textbooks by these students.Initially,simple random samples of 25 undergraduate students and 25 graduate students were taken.The sample standard deviations for the amounts spent were $45 and $64,respectively.A 95% confidence interval for the overall population mean that extends $6 on each side of the sample point estimate is required.Estimate the total number of additional sample observations needed to achieve this goal under proportional allocation.

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. -An automobile company with 3500 employees needs to take a simple random sample in order to estimate the employee population's average satisfaction level on a scale of 0-100.From previous experience,it is estimated that the population standard deviation is approximately 8.0.A 95 % confidence interval for the population mean must extend 3.0 on each side of the sample mean.How many employees need to be sampled to achieve this objective?

A smaller sample size is required where greater population variability exists.

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. -A bank holds 750 delinquent mortgages in residential properties.It requires an estimate of the mean current appraised value of these properties.Initially,a random sample of 25 was appraised,and a sample standard deviation of $38,400 was found.If the bank requires a 90% confidence interval for the population mean extending $5,000 on each side of the sample mean,how many more properties must be appraised?

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. -A questionnaire was mailed to 1000 registered municipal voters selected at random.Only 600 questionnaires were returned,and of the 600 returned,450 respondents were strongly opposed to a surcharge proposed to support the city's Parks and Recreation Department.Can the 75% figure be accepted as a valid estimate of the percentage in the city who are opposed to the surcharge?

Suppose that for a sample of 65 observations from a population of 500,the sample mean is 25.6 and the sample standard deviation is 2.8.Create a 90% confidence interval for the population mean.

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 proportion of all invoices that are from out-of-state suppliers.

A sales representative has 600 accounts.He wants to take a random sample to determine the mean amount of yearly sales for these accounts.From past research,he knows that the population standard deviation is approximately $28,000.How large a sample should he take in order to estimate the population mean within $8,000 at a 98% level of confidence?

Stratified random sampling is an example of a nonprobabilistic sampling method.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: An auditor,examining a total of 650 accounts receivable by a corporation,selected a random sample of 45 accounts.The sample mean is $108.34 and the sample standard deviation is $30.85. -Find a 95% confidence interval for the population mean.

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 95% confidence interval for the total sales.

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 optimum allocation scheme,assuming that the stratum population standard deviations are the same as the corresponding sample values.

Since sample members are geographically close to one another within clusters,their contact by interviewers is relatively expensive.

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 the undergraduate students on the campus.

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. -Find a 90% confidence interval for the population.

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. -A city is divided into 50 geographic subdivisions.An estimate of the proportion of households in the city interested in a new lawn-care service was required.A random sample of three subdivisions contained 610,520,and 730 households,respectively.The households expressing interest in the service were 125,130,and 175,respectively.Find a 90% confidence interval for the proportion of all households in the city interested in the lawn-care service.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: An auditor,examining a total of 650 accounts receivable by a corporation,selected a random sample of 45 accounts.The sample mean is $108.34 and the sample standard deviation is $30.85. -Using an unbiased estimation procedure,find an estimate of the variance of the population mean.