Exam 8: Confidence Interval Estimation

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

A university system enrolling hundreds of thousands of students is considering a change in the way students pay for their education.Currently, the students pay $400 per credit hour. The university system administrators are contemplating charging each student a set fee of $7,000 per quarter, regardless of how many credit hours each takes.To see if this proposal would be economically feasible, the administrators would like to know how many credit hours, on the average, each student takes per quarter.A random sample of 250 students yields a mean of 14.1 credit hours per quarter and a standard deviation of 2.3 credit hours per quarter.Suppose the administration wanted to estimate the mean to within 0.1 hours at 95% reliability and assumed that the sample standard deviation provided a good estimate for the population standard deviation.How large a total sample would they need to take?

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, -True or False: Referring to Scenario 8-4, a 99% confidence interval will contain 99% of the voltages for all such power packs.

An economist is interested in studying the incomes of consumers in a particular 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?

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. -True or False: Referring to Scenario 8-7, a 95% confidence interval for the mean number of rooms rented daily in a given month is narrower than a 99% confidence interval.

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.What value will be used as the point estimate for The mean endowment of all private colleges in the United States?

SCENARIO 8-9 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". -True or False: Referring to Scenario 8-9, a confidence interval estimate of the population proportion would only be valid if the distribution of the number of students who feel comfortable reporting cheating by their fellow students is normal.

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. -True or False: Referring to Scenario 8-7, the parameter of interest is the mean number of rooms rented daily in a given month.

SCENARIO 8-3 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. -True or False: Referring to Scenario 8-3, for the confidence interval to be valid, it is necessary that test scores of students in the special study program on the actuarial exam be normally distributed.

A confidence interval was used to estimate the proportion of statistics students who are Females.A random sample of 72 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?

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. -True or False: Referring to Scenario 8-10, a 95% confidence interval will contain 95% of the population proportion of managers who have caught salespeople cheating on an expense report.

SCENARIO 8-6 After an extensive advertising campaign, the manager of a company wants to estimate the proportion of potential customers that recognize a new product.She samples 120 potential consumers and finds that 54 recognize this product.She uses this sample information to obtain a 95% confidence interval that goes from 0.36 to 0.54. -True or False: Referring to Scenario 8-6, 95% of the time, the sample proportion of people that recognize the product will fall between 0.36 and 0.54.

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?

SCENARIO 8-9 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". -True or False: Referring to Scenario 8-9, a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

True or False: A random sample of 50 provides a sample mean of 31 with a standard deviation of S = 14.The upper bound of a 90% confidence interval estimate of the population mean is 34.32.

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?