Exam 8: Confidence Interval Estimation

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, 95% of the salary offers are between 47.19 and 52.61.

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 proportion of the student population who feel comfortable reporting cheating by their fellow students.

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 $\pm 3$ percentage points. -Referring to Scenario 8-11, the sampling error is 3%.

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, 95% of the people will recognize the product between 36% and 54% of the time.

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

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 mean number of students in the population who own a personal computer.

The confidence interval estimate of the population proportion is constructed around the sample proportion.

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.

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, 95% of the sample means will fall between the computed lower and upper limit of the 95% confidence interval for the mean number of times the handles have been used to lift the bottles before they break.

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, a 99% confidence interval for the mean of the population from the same sample would be wider than 47.19 to 52.61.

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 the mean numbers of student population who own a personal computer is between 0.7911 and 0.8769.

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 population proportion of managers who have caught salespeople cheating on an expense report.

The difference between the lower limit of a confidence interval and the point estimate used in constructing the confidence interval 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 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 sampling error of a 99% confidence interval for the proportion of student population who feel comfortable reporting cheating by their fellow students is __________.

SCENARIO 8-1 The managers of a company are worried about the morale of their employees. In order 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, due to financial limitations, the managers decide to take a sample of 45 employees. This yields a mean score of 88.0 points. A 90% confidence interval would go from ________ to ________.

SCENARIO 8-2 A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired mean length of the insulation is 12 feet. It is known that the standard deviation in the cutting length is 0.15 feet. A sample of 70 cut sheets yields a mean length of 12.14 feet. This sample will be used to obtain a 99% confidence interval for the mean length cut by machine. -Referring to Scenario 8-2, suppose the engineer had decided to estimate the mean length to within 0.03 with 99% confidence. Then the sample size would be ________.

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

The county clerk wants to estimate the proportion of voters who will need special election facilities. The clerk wants to construct a 95% confidence interval for the population proportion which extends at most 0.07 to either side of the sample proportion. How large a sample must be taken to assure these conditions are met?

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 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 8-12-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 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-B.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 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-B, it is possible that the mean of the population will fall between the computed lower and upper limit of the 95% confidence interval for the mean number of times the handles have been used to lift the bottles before they break.