Exam 8: Confidence Interval Estimation

TABLE 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 Table 8-4,a confidence interval for this sample would be based on the t distribution with ________ degrees of freedom.

TABLE 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 Table 8-10,the critical value for a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report is ________.

TABLE 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 Table 8-6,95% of the time,the sample proportion of people that recognize the product will fall between 0.36 and 0.54.

TABLE 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 Table 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 ________.

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.

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.The 95% confidence interval for π is 0.59 ± 0.07.Interpret this interval.

TABLE 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 Table 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.

TABLE 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. -Referring to Table 8-7,a 99% confidence interval for the mean number of rooms rented daily in a given month is from ________ to ________.

TABLE 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 Table 8-10,the sampling error of a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report is ________.

TABLE 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. -True or False: Referring to Table 8-5,95% of the salary offers are between 47.19 and 52.61.

TABLE 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. -True or False: Referring to Table 8-1,this confidence interval is only valid if the scores on the Fortunato test are normally distributed.

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 ________.

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?

The t distribution

True or False: The confidence interval estimate of the population proportion is constructed around the sample proportion.

It is desired to estimate the mean total compensation of CEOs in the Service industry.Data were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be ($2,181,260,$5,836,180).Which of the following interpretations is correct?

TABLE 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. -True or False: Referring to Table 8-2,the confidence interval indicates that the machine is not working properly.

TABLE 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 Table 8-10,construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report.

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

TABLE 8-13 A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburban county in Houston.His main concern is the total market value of the 3,605 houses in the suburban county.He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample mean market price of $225,000 and a sample standard deviation of $38,700.The consulting group also found out that the mean differences between market prices and appraised prices was $125,000 with a standard deviation of $3,400.Also the proportion of houses in the sample that are appraised for higher than the market prices is 0.24. -Referring to Table 8-13,what will be the 90% confidence interval for the population proportion of houses that will be appraised for higher than the market prices?