Exam 8: Confidence Interval Estimation

Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses.Much of this money is put into a fund called an endowment,and the college spends only the interest earned by the fund.A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars): 60.2,47.0,235.1,490.0,122.6,177.5,95.4,and 220.0.Summary statistics yield x? =180.975 and S = 143.042 .Calculate a 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments.

SCENARIO 8-7 A hotel chain wants to estimate the mean number of rooms rented daily in a given month.The population of rooms rented daily is assumed to be normally distributed for each month with a standard deviation of 240 rooms.During February,a sample of 25 days has a sample mean of 370 rooms. -Referring to Scenario 8-7,it is possible that the 99% confidence interval calculated from the data will not contain the population mean number of rooms rented daily in a given month.

SCENARIO 8-4 The actual voltages of power packs labeled as 12 volts are as follows: 11.77,11.90,11.64,11.84,12.13,11.99,and 11.77. -Referring to Scenario 8-4,a confidence interval for this sample would be based on the t distribution with _____degrees of freedom.

SCENARIO 8-12 The Three Brothers Energy Drink Company bottles and distributes a popular drink for athletes and exercise enthusiasts.Because of its marketing successes the company has installed an additional filling machine and the managers are eager to use it in daily operations.The machine is set to fill bottles at 16 oz. However,we know there is inherent machine variability and quality control has determined through testing a mean of 16.2 oz.and a standard deviation of 0.3 oz.using a 100 bottle sample. -Refer to Scenario 8-12. In calculating a 90% confidence interval for the population what would be the sampling error?

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.

SCENARIO 8-10 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 Scenario 8-10,the sampling error of a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report is .

SCENARIO 8-10 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 Scenario 8-10,it is possible that the 95% confidence interval calculated from the data will not contain the sample proportion of managers who have caught salespeople cheating on an expense report.

SCENARIO 8-12 The Three Brothers Energy Drink Company bottles and distributes a popular drink for athletes and exercise enthusiasts.Because of its marketing successes the company has installed an additional filling machine and the managers are eager to use it in daily operations.The machine is set to fill bottles at 16 oz. However,we know there is inherent machine variability and quality control has determined through testing a mean of 16.2 oz.and a standard deviation of 0.3 oz.using a 100 bottle sample. -Refer to Scenario 8-12. If we select using a 95% confidence interval in lieu of a 90% one for the mean fill volume,the new interval would be narrower.

If you were constructing a 99% confidence interval of the population mean based on a sample of n=25 where the standard deviation of the sample S = 0.05,the critical value of t will be

The head librarian at the Library of Congress 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 for a 95% confidence interval,approximately how large a sample did her assistant use to determine the interval estimate?

SCENARIO 8-4 The actual voltages of power packs labeled as 12 volts are as follows: 11.77,11.90,11.64,11.84,12.13,11.99,and 11.77. -Referring to Scenario 8-4,a 99% confidence interval for the mean voltage of the power packs is from_____ to_____ .

An economist is interested in studying the incomes of consumers in a country.The population standard deviation is known to be $1,000.A random sample of 50 individuals resulted in a mean income of $15,000.What is the width of the 90% confidence interval?

The head librarian at the Library of Congress 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.What is an efficient,unbiased point estimate of the number of books checked out each day at the Library of Congress?

In estimating the population mean with the population standard deviation unknown,if the sample size is 12,there will be 6 degrees of freedom.

SCENARIO 8-11 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 Scenario 8-11,the standard error is 3%.

SCENARIO 8-10 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 Scenario 8-10,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.

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.

The difference between the sample mean and the population mean is called the sampling error.

SCENARIO 8-9 A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students.A survey 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 Scenario 8-9,we are 99% confident that the total number of the student population who feel comfortable reporting cheating by their fellow students is between 0.4557 and 0.5043.

SCENARIO 8-5 A sample of salary offers (in thousands of dollars)given to management majors is: 48,51,46,52,47,48,47,50,51,and 59.Using this data to obtain a 95% confidence interval resulted in an interval from 47.19 to 52.61. -Referring to Scenario 8-5,it is possible that the mean of the population is between 47.19 and 52.61.