Exam 8: Confidence Interval Estimation

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,construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople listing a "strip bar" as a restaurant on an expense report.

When determining the sample size for a proportion for a given level of confidence and sampling error,the closer to 0.50 that π is estimated to be,the sample size required

It is desired to estimate the average total compensation of CEOs in the Service industry.Data were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be ($2,181,260,$5,836,180).Which of the following interpretations is correct?

Instruction 8-11 The principal of a high school of a small suburb wants to make sure that no more than 5% of the students skip more than 10 days of school in a year.A random sample of 145 students from a population of 800 showed that 12 students skipped more than 10 days of school last year. -Referring to Instruction 8-11,what is the upper bound of the 95% one-sided confidence interval for the proportion of students who skipped more than 10 days of school last year?

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 proportion of student population who own a personal computer.

Instruction 8-5 The actual voltages of power packs labelled as 12 volts are as follows: 11.77,11.90,11.64,11.84,12.13,11.99,and 11.77. -Referring to Instruction 8-5,a 99% confidence interval will contain 99% of the voltages for all such power packs.

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,a 90% confidence interval for the mean score of actuarial students in the special program is from ________ to ________.

Instruction 8-9 A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburb of Sydney.His main concern is the total market value of the 3,605 houses in the suburb.From past experience,the standard deviation of market housing prices is estimated to be $81,000.He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample average market price of $450,000 and a sample standard deviation of $77,400.The consulting group also found out that the average differences between market prices and appraised prices was $250,000 with a standard deviation of $6,800.Also the proportion of houses in the sample that are appraised for higher than the market prices is 0.24. -Referring to Instruction 8-9,if he wants a 95% confidence on estimating the true population average market price of the houses in the suburb to be within $20,000,how large a sample will he need?

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 mean of the sample is ________,while the standard deviation of the sample is ________.

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).Based on the interval above,is the population proportion of females equal to 0.60?

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 critical value used in constructing a 90% confidence interval is ________.

Private colleges rely on money contributed by individuals for much of their major building expenses.Much of this money is put into a fund called a trust,and the college spends only the interest earned by the fund.A recent survey of 8 private colleges in Australia revealed the following trusts (in millions of dollars): 60.2,47.0,235.1,490.0,122.6,177.5,95.4,and 220.0.What value will be used as the point estimate for the mean trust of all private colleges in Australia?

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 goes from ________ to ________.

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,the sampling error is 3%.

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 critical value for a 99% confidence interval for this sample is ________.

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 giving a kickback to a customer is ________.

The difference between the upper limit of a confidence interval and the point estimate used in constructing the confidence interval is called the sampling error.

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,we are 99% confident that the total numbers of student population who feel comfortable reporting cheating by their fellow students is between 0.4557 and 0.5043.

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 between 27.5 and 30.3.

The width of a confidence interval equals twice the sampling error.