Exam 8: Confidence Interval Estimation

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. -True or False: Referring to Scenario 8-11, the size of the population is 1,500.

True or False: A population parameter is used to estimate a confidence interval.

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, it is possible that the true proportion of people that recognize the product is between 0.36 and 0.54.

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 95% confidence interval for the mean voltage of the power pack is wider than a 99% confidence interval.

SCENARIO 8-8 The president of a university would like to estimate the proportion of the student population that owns a personal computer.In a sample of 500 students, 417 own a personal computer. -True or False: Referring to Scenario 8-8, 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.

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 proportion of people that recognize the product will fall between 0.36 and 0.54.

True or False: For a given data set, the confidence interval will be wider for 95% confidence than for 90% confidence.

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. -True or False: Referring to Scenario 8-11, the standard error is 3%.

When determining the sample size necessary for estimating the true population mean, which Factor is not considered when sampling with replacement?

True or False: The width of a confidence interval equals twice the sampling error.

True or False: The sampling error can either be positive or negative.

True or False: Holding the width of a confidence interval fixed, increasing the level of confidence can be achieved with a lower sample size.

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, 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% if you do not have the information on the 49% in the interviews who said that they would purchase the new game?

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

True or False: The standardized normal distribution is used to develop a confidence interval estimate of the population proportion regardless of whether the population standard deviation is known.

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 99% confidence interval will contain 99% of the student population who feel comfortable reporting cheating by their fellow students.

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, it is possible that the confidence interval obtained will not contain the mean score for all actuarial students in the special study program.

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, this interval requires the assumption that the distribution of the number of people recognizing the product has a normal distribution.

In the construction of confidence intervals, if all other quantities are unchanged, an increase In the sample size will lead to a 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.If the head librarian knows that the Population standard deviation is 150 books checked out per day, approximately how large a Sample did her assistant use to determine the interval estimate?