Exam 8: Confidence Interval Estimation

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 working a second job on company time is __________.

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 It is possible that a 90% confidence interval will not include the mean fill volume.

A prison official wants to estimate the proportion of cases of recidivism.Examining the records of 250 convicts, the official determines that there are 65 cases of recidivism.A 99% confidence interval for the proportion of cases of recidivism would go from __________ to __________.

Suppose a 95% confidence interval for turns out to be (1,000, 2,100).Give a definition of what it means to be "95% confident" as an inference.

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

The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown.

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

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?

Which of the following statements is(are)correct concerning a 95% confidence interval?

Suppose a 95% confidence interval for has been constructed.If it is decided to take a larger sample and to decrease the confidence level of the interval, then the resulting interval width would .(Assume that the sample statistics gathered would not change very much for the new sample.)

SCENARIO 8-1 The managers of a company are worried about the morale of their employees.To determine if a problem in this area exists, they decide to evaluate the attitudes of their employees with a standardized test.They select the Fortunato test of job satisfaction, which has a known standard deviation of 24 points. -Referring to Scenario 8-1, this confidence interval is only valid if the scores on the Fortunato test are normally distributed.

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?

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. -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. -Referring to Scenario 8-6, the parameter of interest is 54/120 = 0.45.

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. -Referring to Scenario 8-8, we are 99% confident that between 79.11% and 87.69% of the student population own a personal computer.

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, the sampling error of a 99% confidence interval for the proportion of student population who feel comfortable reporting cheating by their fellow students is __________.

A prison official wants to estimate the proportion of cases of recidivism.Examining the records of 250 convicts, the official determines that there are 65 cases of recidivism.A confidence interval will be obtained for the proportion of cases of recidivism.Part of this calculation includes the estimated standard error of the sample proportion.For this sample, the estimated standard error is __________.

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.

The sampling error can either be positive or negative.

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, a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.