Exam 8: Confidence Interval Estimation

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 8-4 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 estimate of the population mean would only be valid if the distribution of voltages is normal.

Given a sample mean of 2.1 and a sample standard deviation of 0.7 from a sample of 10 data points, a 90% confidence interval will have a width of 2.36.

In forming a 90% confidence interval for a population mean from a sample size of 22, the number of degrees of freedom from the t distribution equals 22.

SCENARIO 8-13-B You are the quality control manager of a water bottles company. One of the biggest complaints in the past years has been the breakage and, hence, the concern on the durability of the connector between the lid and the bottle which many users use as a handle for the bottles. To collect evidence before implementing any modification to the production process, your department has subjected 50 water bottle to durability test and the following data on the number of times the handles have been used to lift the bottles before they break are contained in the file Scenario8-13-DataB.XLSX. 493 506 515 491 500 505 517 510 506 503 503 491 495 496 496 505 493 486 504 483 514 494 497 501 493 490 510 494 494 495 494 486 495 506 506 507 502 498 510 501 500 505 492 486 501 496 501 521 510 498 Assume that the population standard deviation is 5 and the number of times the handles have been used to lift the bottles before they break follows a normal distribution. -Referring to Scenario 8-13-B, the width of the 95% confidence interval for the mean number of times the handles have been used to lift the bottles before they break is _____.

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.

The t distribution

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, this interval requires the use of the t distribution to obtain the confidence coefficient.

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". -Referring to Scenario 8-9, the parameter of interest is the total number of students in the population who feel comfortable reporting cheating by their fellow students.

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 cheating on an expense report.

SCENARIO 8-12-A You are the quality control manager of a water bottles company. One of the biggest complaints in the past years has been the breakage and, hence, the concern on the durability of the connector between the lid and the bottle which many users use as a handle for the bottles. To collect evidence before implementing any modification to the production process, your department has subjected 50 water bottles to a durability test and the following data on the number of times the handles have been used to lift the bottles before they break are contained in the file SCENARIO 8-12-A.XLSX. 495 499 502 500 491 498 498 495 488 516 513 486 504 503 493 504 489 500 495 499 501 507 511 496 486 497 510 504 493 482 511 502 520 514 486 514 500 505 512 500 504 498 503 514 474 489 488 506 517 490 Assume that and the number of times the handles have been used to lift the bottles before they break follows a normal distribution. -Referring to Scenario 8-12-A, the critical value used to construct the 95% confidence interval for the mean number of times the handles have been used to lift the bottles before they break is _____.

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, the parameter of interest is the proportion of the student population who own a personal computer.

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?

Sampling error equals half the width of a confidence interval.

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 giving a kickback to a customer is __________.

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

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. -Referring to Scenario 8-3, the confidence interval will be based on __________ degrees of freedom.

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 working a second job on company time.

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. -Referring to Scenario 8-3, a 90% confidence interval for the mean score of actuarial students in the special program is from __________ to __________.

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