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,determine the sample size needed to estimate the proportion of managers who have caught employees working a second job on company time to within ±0.02 with 95% confidence.

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,we do not know for sure whether the true population mean is between 5.623 and 6.377 lawnmowers sold.

A population parameter is used to estimate a confidence interval.

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 is valid only if the lengths cut are normally distributed.

Instruction 8-14 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 8-14,the parameter of interest is 54/120 = 0.45.

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 population proportion of houses that will be appraised for higher than the market prices?

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

Instruction 8-12 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 8-12,what will be the 90% confidence interval for the average market price of the houses in the suburb constructed by the consulting group?

When using a one-sided confidence interval,an auditor would conclude that a company is not in compliance with the internal control if the tolerable exception rate is higher than the upper bound.

Instruction 8-22 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 8-22,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?

A university dean is interested in determining the proportion of students who receive some sort of financial aid.Rather than examine the records for all students,the dean randomly selects 200 students and finds that 118 of them are receiving financial aid.If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability,how many students would need to be sampled?

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 95% confidence interval for the proportion of student population who feel comfortable reporting cheating by their fellow students is 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,it is possible that the 99% confidence interval calculated from the data will not contain the sample proportion of students who own a personal computer.

Instruction 8-14 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 8-14,95% of the time,the sample proportion of people that recognise the product will fall between 0.36 and 0.54.

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,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.

Suppose a 95% confidence interval for μ turns out to be (1,000,2,100).What type of reasoning would you make when defining what "95% confident" means about the population?

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,a confidence interval estimate of the population proportion would only be valid if the distribution of the number of students who own a personal computer is normal.

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 listing a "strip bar" as a restaurant on an expense report is ________.

A university dean is interested in determining the proportion of students who receive some sort of financial aid.Rather than examine the records for all students,the dean randomly selects 200 students and finds that 118 of them are receiving financial aid.Use a 90% confidence interval to estimate the true proportion of students who receive financial aid.

The t distribution approaches the standardised normal distribution when the number of degrees of freedom increases.