Exam 8: Confidence Interval Estimation

A university dean is interested in determining the proportion of students who receive some sort of financial aid.Rather than examine the records for all students,the dean randomly selects 200 students and finds that 118 of them are receiving financial aid.If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability,how many students would need to be sampled?

A university dean is interested in determining the proportion of students who receive some sort of financial aid.Rather than examine the records for all students,the dean randomly selects 200 students and finds that 118 of them are receiving financial aid.Use a 90% confidence interval to estimate the true proportion of students who receive financial aid.

Instruction 8-4 To become an actuary,it is necessary to pass a series of 10 exams,including the most important one,an exam in probability and statistics.An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program.They take a sample of 8 actuarial students in this program and determine that their scores are: 2,5,8,8,7,6,5,and 7.This sample will be used to calculate a 90% confidence interval for the mean score for actuarial students in the special study program. -Referring to Instruction 8-4,the confidence interval will be based on ________ degrees of freedom.

Instruction 8-10 The Registrar of a university would like to estimate the proportion of the student population who owns a personal computer.In a sample of 500 students,417 own a personal computer. -Referring to Instruction 8-10,the parameter of interest is the proportion of student population who own a personal computer.

The sample mean is a point estimate of the population mean.

A sample size of 5 provides a sample mean of 9.6.If the population variance is known to be 5 and the population distribution is assumed to be normal,the lower limit for a 90% confidence interval is 7.96.

The difference between the sample proportion and the population proportion is called the sampling error.

Other things being equal,as the confidence level for a confidence interval increases,the width of the interval increases.

Instruction 8-14 A sales and marketing management magazine conducted a survey on salespeople cheating on their expense reports and other unethical conduct.In the survey on 200 managers,58% of the managers have caught salespeople cheating on an expense report,50% have caught salespeople working a second job on company time,22% have caught salespeople listing a "strip bar" as a restaurant on an expense report,and 19% have caught salespeople giving a kickback to a customer. -Referring to Instruction 8-14,it is possible that the 95% confidence interval calculated from the data will not contain the sample proportion of managers who have caught salespeople cheating on an expense report.

For a t distribution with 12 degrees of freedom,the area between -2.6810 and 2.1788 is 0.980.

Instruction 8-1 A random sample of 100 stores from a large chain of 1,000 garden supply stores was selected to determine the average number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated an average of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results. -Referring to Instruction 8-1,of all possible samples of 100 stores taken from the population of 1,000 stores,95% of the confidence intervals developed will contain the true population mean within the interval.

Instruction 8-14 A sales and marketing management magazine conducted a survey on salespeople cheating on their expense reports and other unethical conduct.In the survey on 200 managers,58% of the managers have caught salespeople cheating on an expense report,50% have caught salespeople working a second job on company time,22% have caught salespeople listing a "strip bar" as a restaurant on an expense report,and 19% have caught salespeople giving a kickback to a customer. -Referring to Instruction 8-14,it is possible that the 95% confidence interval calculated from the data will not contain the population proportion of managers who have caught salespeople cheating on an expense report.

Instruction 8-14 A sales and marketing management magazine conducted a survey on salespeople cheating on their expense reports and other unethical conduct.In the survey on 200 managers,58% of the managers have caught salespeople cheating on an expense report,50% have caught salespeople working a second job on company time,22% have caught salespeople listing a "strip bar" as a restaurant on an expense report,and 19% have caught salespeople giving a kickback to a customer. -Referring to Instruction 8-14,we are 95% confident that between 51.16% and 64.84% of managers in the population have caught salespeople cheating on an expense report.

Instruction 8-13 A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students.A surveyed of 2,800 students was conducted and the students were asked if they felt comfortable reporting cheating by their fellow students.The results were 1,344 answered "YES" and 1,456 answered "NO". -Referring to Instruction 8-13,a 95% confidence interval for the proportion of student population who feel comfortable reporting cheating by their fellow students is narrower than a 99% confidence interval.

Instruction 8-4 To become an actuary,it is necessary to pass a series of 10 exams,including the most important one,an exam in probability and statistics.An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program.They take a sample of 8 actuarial students in this program and determine that their scores are: 2,5,8,8,7,6,5,and 7.This sample will be used to calculate a 90% confidence interval for the mean score for actuarial students in the special study program. -Referring to Instruction 8-4,for the confidence interval to be valid,it is necessary that test scores of students in the special study program on the actuarial exam be normally distributed.

Instruction 8-14 A sales and marketing management magazine conducted a survey on salespeople cheating on their expense reports and other unethical conduct.In the survey on 200 managers,58% of the managers have caught salespeople cheating on an expense report,50% have caught salespeople working a second job on company time,22% have caught salespeople listing a "strip bar" as a restaurant on an expense report,and 19% have caught salespeople giving a kickback to a customer. -Referring to Instruction 8-14,a 95% confidence interval will contain 95% of the population proportion of managers who have caught salespeople cheating on an expense report.

Suppose a department store wants to estimate the average age of the customers of its contemporary apparel department,correct to within 2 years,with level of confidence equal to 95%.Management believes that the standard deviation is 8 years.The sample size they should take is ________.

Instruction 8-13 A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students.A surveyed of 2,800 students was conducted and the students were asked if they felt comfortable reporting cheating by their fellow students.The results were 1,344 answered "YES" and 1,456 answered "NO". -Referring to Instruction 8-13,the sampling error of a 99% confidence interval for the proportion of student population who feel comfortable reporting cheating by their fellow students is ________.

Instruction 8-3 A quality control engineer is interested in the mean length of timber poles being cut automatically by machine.The desired length of the insulation is 12 metres.It is known that the standard deviation in the cutting length is 0.15 metres.A sample of 70 cut poles yields a mean length of 12.14 metres.This sample will be used to obtain a 99% confidence interval for the mean length cut by machine. -Referring to Instruction 8-3,the confidence interval indicates that the machine is not working properly.

Instruction 8-10 The Registrar of a university would like to estimate the proportion of the student population who owns a personal computer.In a sample of 500 students,417 own a personal computer. -Referring to Instruction 8-10,it is possible that the 99% confidence interval calculated from the data will not contain the sample proportion of students who own a personal computer.