Exam 8: Confidence Interval Estimation

Instruction 8-20 A business and management magazine conducted a survey on employees cheating on their expense reports and other unethical conduct. In the survey of 200 managers, 58% of the managers have caught employees cheating on an expense report, 50% have caught employees working a second job on company time, 22% have caught employees listing a "strip bar" as a restaurant on an expense report, and 19% have caught employees giving a kickback to a customer. -Referring to Instruction 8-20,construct a 95% confidence interval estimate of the population proportion of managers who have caught employees working a second job on company time.

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 time,the sample mean salary offer to students majoring in management will fall between 27.5 and 30.3.

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 8-10 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 8-10,a confidence interval for this sample would be based on the t distribution with____________ degrees of freedom.

Instruction 8-9 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 8-9,a 90% confidence interval for the mean score of actuarial students in the special program is from____________ to ____________.

Instruction 8-18 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 8-18,what is the needed sample size to obtain a 95% confidence interval in estimating the percentage of the targeted young adults who will purchase the new game to within ±5%?

The collection and evaluation of evidence about information relating to an economic entity in order to determine and report on how well the information corresponds to established criteria is known as ________.

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

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 critical value to use in obtaining the confidence interval is _________ .

When determining the sample size necessary for estimating the true population mean,which factor is NOT considered when sampling with replacement?

The t distribution allows the calculation of confidence intervals for means when the actual standard error is not known.

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.

A 99% confidence interval estimate can be interpreted to mean that

An economist is interested in studying the incomes of consumers in a particular region.The population standard deviation is known to be $2,000.A random sample of 50 individuals resulted in an average income of $30,000. -What is the upper end point in a 99% confidence interval for the average income?

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.

An economist is interested in studying the incomes of consumers in a particular region.The population standard deviation is known to be $2,000.A random sample of 50 individuals resulted in an average income of $30,000. -What is the width of the 90% confidence interval?

Instruction 8-16 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 8-16,we are 99% confident that between 79.11% and 87.69% of the student population own a personal computer.

Instruction 8-19 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 8-19,we are 99% confident that between 45.57% and 50.43% of the student population feel comfortable reporting cheating by their fellow students.

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 all confidence intervals constructed similarly to this one will contain the mean of the population.

The head of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option.Suppose there is no information about the proportion of students who might choose the option.What size sample should the department head take if she wants to be 95% confident that the estimate is within 0.10 of the true proportion?