Exam 8: Confidence Interval Estimation

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

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?

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, 1,500 is the size of the

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

True or False: 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.

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).Based on the interval above, do you believe the mean total Compensation of CEOs in the Service industry is more than $3,000,000?

True or False: 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.

True or False: A sample of 100 fuses from a very large shipment is found to have 10 that are defective.The 95% confidence interval would indicate that, for this shipment, the proportion of defective fuses is between 0 and 0.28.

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 use of the t distribution to obtain the confidence coefficient.

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. -True or False: Referring to Scenario 8-5, the confidence interval obtained is valid only if the distribution of the population of salary offers is normal.

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, they should sample ________ employees if they want to estimate the mean score of the employees within 5 points with 90% confidence.

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

True or False: The t distribution allows the calculation of confidence intervals for means for small samples when the population variance is not known, regardless of the shape of the distribution in the population.

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, it is possible that the 99% confidence interval calculated from the data will not contain the sample proportion of students who own a personal computer.

True or False: A race car driver tested his car for time from 0 to 60 mph, and for 20 tests obtained a mean of 4.85 seconds with a standard deviation of 1.47 seconds.A 95% confidence interval for the 0 to 60 mean time is 4.52 seconds to 5.18 seconds.

When determining the sample size for a proportion for a given level of confidence and Sampling error, the closer to 0.50 that π is estimated to be, the sample size required __________.

True or False: In estimating the population mean with the population standard deviation unknown, if the sample size is 12, there will be 6 degrees of freedom.

An economist is interested in studying the incomes of consumers in a particular country.The Population standard deviation is known to be $1,000.A random sample of 50 individuals Resulted in a mean income of $15,000.What total sample size would the economist need to Use for a 95% confidence interval if the width of the interval should not be more than $100?

SCENARIO 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 Scenario 8-7, a 99% confidence interval will contain 99% of the sample mean number of rooms rented daily in a given month.

True or False: Holding the level of confidence fixed, increasing the sample size will lead to a wider confidence interval.