Exam 8: Confidence Interval Estimation

A major department store chain is interested in estimating the mean amount its credit card customers spent on their first visit to the chain's new store in the mall.Fifteen credit card accounts were randomly sampled and analyzed with the following results: and S = 20 .Assuming the distribution of the amount spent on their first visit is normal, what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for

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, the sampling error is 3%.

A quality control engineer is interested in estimating the proportion of defective items coming off a production line.In a sample of 300 items, 27 are defective.A 90% confidence interval for the proportion of defectives from this production line would go from __________ to __________.

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

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, the standard error is 3%.

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. -Referring to Scenario 8-7, the sampling error of a 99% confidence interval for the mean number of rooms rented daily in a given month is __________.

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, if we use the same sample information to obtain a 95% confidence interval, the resulting interval would be narrower than the one obtained here with 90% confidence.

A confidence interval was used to estimate the proportion of statistics students who are females.A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642).Based on the interval above, is the population proportion of females equal to 0.60?

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

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

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 for this sample would be based on the t distribution with __________ degrees of freedom.

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.

As an aid to the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period.The director randomly selects 64 different 24-hour periods and determines the number of admissions for each.For this sample, and S = 100.Estimate the mean number of admissions per 24-hour period with a 95% confidence interval.

Holding the sample size fixed, increasing the level of confidence in a confidence interval will necessarily lead to a wider confidence interval.

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 99% confidence interval for the mean voltage of the power packs is 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 8-1 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, 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, the critical value to use in obtaining the confidence interval is ________.

The t distribution is used to develop a confidence interval estimate of the population proportion when the population standard deviation is unknown.