Exam 8: Confidence Interval Estimation

Instruction 8-2 The managers of a company are worried about the morale of their employees. In order to determine if a problem in this area exists, they decide to evaluate the attitudes of their employees with a standardised test. They select the Fortunato test of job satisfaction, which has a known standard deviation of 24 points. -Referring to Instruction 8-2,this confidence interval is only valid if the scores on the Fortunato test are normally distributed.

The t distribution allows the calculation of confidence intervals for means for small samples when the population variance is not known,regardless of the shape of the distribution in the population.

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,it is possible that the 95% confidence interval calculated from the data will not contain the population proportion of managers who have caught employees cheating on an expense report.

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,we are 95% confident that between 51.16% and 64.84% of managers in the population have caught employees cheating on an expense report.

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,the confidence interval will be based on__________degrees of freedom.

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

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

Statistical sampling is widely used for the purposes of estimation in auditing due to its many advantages.Which of the following is NOT an advantage of statistical sampling in auditing?

An officer with the Australian Electoral Office wants to estimate the proportion of retired voters who will need special election facilities.The officer wants to find a 95% confidence interval for the population proportion which extends at most 0.07 to either side of the sample proportion.How large a sample must be taken to assure these conditions are met?

Instruction 8-15 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 8-15,what will be the 90% confidence interval for the total difference between the market prices and appraised prices of the houses in the suburb constructed by the consulting group?

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,the sampling error of a 95% confidence interval estimate of the population proportion of managers who have caught employees working a second job on company time 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 8-11 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 8-11,the confidence interval obtained is valid only if the distribution of the population of salary offers is normal.

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 8-5 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 90% confidence interval calculated from the same data would be narrower than a 99% 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,the critical value for a 99% confidence interval for this sample is________

Instruction 8-17 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 8-17,what is the critical value for the 95% one-sided confidence interval for the proportion of students who skipped more than 10 days of school last year?

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,the sampling error of a 99% confidence interval for the proportion of student population who own a personal computer is ________

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,a 99% confidence interval for the mean of the population from the same sample would be wider than 27.5 to 30.3.

A quality control engineer is interested in estimating the proportion of defective items coming off a production line.In a sample of 300 items,27 are defective.A 90% confidence interval for the proportion of defectives from this production line would go from ________to________.