Exam 8: Confidence Interval Estimation

The head librarian at the National Library of Australia has asked her assistant for an interval estimate of the mean number of books checked out each day.The assistant provides the following interval estimate: from 740 to 920 books per day.If the head librarian knows that the population standard deviation is 150 books checked out per day,and she asked her assistant for a 95% confidence interval,approximately how large a sample did her assistant use to determine the interval estimate?

A confidence interval was used to estimate the proportion of business statistics students that are females.A random sample of 72 business statistics students generated the following 90% confidence interval: (0.438,0.642).Using the information above,what total sample size would be necessary if we wanted to estimate the true proportion to within 0.08 using 95% confidence?

Instruction 8-6 A sample of salary offers (in thousands of dollars)given to students majoring in management is: 28,31,26,32,27,28,27,30,31,and 29.Using this data to obtain a 95% confidence interval resulted in an interval from 27.5 to 30.3. -Referring to Instruction 8-6,the confidence interval obtained is valid only if the distribution of the population of salary offers is normal.

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,if we use the same sample information to obtain a 95% confidence interval,the resulting interval would be narrower than the one obtained here with 90% confidence.

Suppose a 95% confidence interval for μ turns out to be (1,000,2,100).Give a definition of what it means to be "95% confident" in an inference.

In forming a 90% confidence interval for a population mean from a sample size of 22,the number of degrees of freedom from the t distribution equals 22.

Instruction 8-6 A sample of salary offers (in thousands of dollars)given to students majoring in management is: 28,31,26,32,27,28,27,30,31,and 29.Using this data to obtain a 95% confidence interval resulted in an interval from 27.5 to 30.3. -Referring to Instruction 8-6,it is possible that the mean of the population is not between 27.5 and 30.3.

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,if the population had consisted of 10,000 stores,the confidence interval estimate of the mean would have been wider in range.

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 confidence interval estimate of the population proportion would only be valid if the distribution of the number of students who feel comfortable reporting cheating by their fellow students is normal.

Instruction 8-7 After an extensive advertising campaign,the manager of a company wants to estimate the proportion of potential customers that recognise a new product.She samples 120 potential consumers and finds that 54 recognise this product.She uses this sample information to obtain a 95% confidence interval that goes from 0.36 to 0.54. -Referring to Instruction 8-7,this interval requires the assumption that the distribution of the number of people recognising the product has a normal distribution.

Instruction 8-12 A poll was conducted by the marketing department of a video game company to determine the popularity of a new game that was targeted to be launched in three months.Telephone interviews with 1,500 young adults were conducted which revealed that 49% said they would purchase the new game.The margin of error was ±3 percentage points. -Referring to Instruction 8-12,you are 99% confident that the percentage of the targeted young adults who will purchase the new game is somewhere between 46% and 52%.

A random sample of 50 provides a sample mean of 31 with a standard deviation of S =14.The upper bound of a 90% confidence interval estimate of the population mean is 34.32.

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,it is possible that the 99% confidence interval calculated from the data will not contain the proportion of student population who feel comfortable reporting cheating by their fellow students.

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,a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

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,a 99% confidence interval will contain 99% of the student population who own a personal computer.

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,the sampling error of a 95% confidence interval estimate of the population proportion of managers who have caught salespeople working a second job on company time is ________.

The t distribution is used to develop a confidence interval estimate of the population proportion when the population standard deviation is unknown.

The standardised normal distribution is used to develop a confidence interval estimate of the population proportion regardless of whether the population standard deviation is known.

A private university is considering a change in the way students pay for their education.Presently the students pay $55 per credit hour.The university system administrators are contemplating charging each student a set fee of $750 per quarter,regardless of how many credit hours each takes.To see if this proposal would be economically feasible,the administrators would like to know how many credit hours,on the average,each student takes per quarter.A random sample of 250 students yields a mean of 14.1 credit hours per quarter and a standard deviation of 2.3 credit hours per quarter.Suppose the administration wanted to estimate the mean to within 0.1 hours at 95% reliability and assumed that the sample standard deviation provided a good estimate for the population standard deviation.How large a sample would they need to take?

Instruction 8-6 A sample of salary offers (in thousands of dollars)given to students majoring in management is: 28,31,26,32,27,28,27,30,31,and 29.Using this data to obtain a 95% confidence interval resulted in an interval from 27.5 to 30.3. -Referring to Instruction 8-6,95% of the sample means will fall between 27.5 and 30.3.