Exam 8: Confidence Interval Estimation

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,we are 99% confident that the average numbers of student population who own a personal computer is between 0.7911 and 0.8769.

Suppose a 95% confidence interval for μ turns out to be (1,000,2,100).To make more useful inferences from the data,it is desired to reduce the width of the confidence interval.Which of the following will result in a reduced interval width?

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,what will be the 90% confidence interval for the population proportion of houses that will be appraised for higher than the market prices?

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 salary offers are between 27.5 and 30.3.

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?

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,what will be the 90% confidence interval for the average market price of the houses in the suburb constructed by the consulting group?

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 listing a "strip bar" as a restaurant on an expense report 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,it is possible that the 99% confidence interval calculated from the data will not contain the sample proportion of students who feel comfortable reporting cheating by their fellow students.

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.

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

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

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 report contains all the essential components for an ethical reporting of poll results.

A sample of 100 fuses from a very large shipment is found to have 10 that are defective.The 95% confidence interval would indicate that,for this shipment,the proportion of defective fuses is between 0 and 0.28.

A point estimate consists of a single sample statistic that is used to estimate the true population parameter.

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,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%?

Given a sample mean of 2.1 and a sample standard deviation of 0.7 from a sample of 10 data points,a 90% confidence interval will have a width of 2.36.

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 to use 25 days of data to construct the interval estimate,what confidence level can she attach to the interval estimate?

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

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 between 45.57% and 50.43% of the student population 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 95% confidence interval for the proportion of student population who own a personal computer is narrower than a 99% confidence interval.