Exam 8: Confidence Interval Estimation

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 8-11 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, you are 99% confidence that the percentage of the targeted young adults who will purchase the new game is somewhere between 46% and 52%.

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 between 79.11% and 87.69% of the student population own a personal computer.

The t distribution approaches the standardized normal distribution when the number of degrees of freedom increases.

SCENARIO 8-12 The Three Brothers Energy Drink Company bottles and distributes a popular drink for athletes and exercise enthusiasts.Because of its marketing successes the company has installed an additional filling machine and the managers are eager to use it in daily operations.The machine is set to fill bottles at 16 oz. However, we know there is inherent machine variability and quality control has determined through testing a mean of 16.2 oz.and a standard deviation of 0.3 oz.using a 100 bottle sample. -Refer to Scenario 8-12.Suppose you want to estimate the population mean fill with 95%confidence and 0.04 oz.sampling error rate.What should be your sample size?

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 size of the population is 1,500.

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.

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 fromto _.

SCENARIO 8-9 A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students.A survey 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, a 90% confidence interval calculated from the same data would be narrower than a 99% 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 working a second job on company time is _.

The t distribution allows the calculation of confidence intervals for means when the actual standard deviation is not known.

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.

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 8-6 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 to the manager is the proportion of potential customers in this sample that recognize the new product.

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, what is the needed sample size to obtain a 90% confidence interval estimate of the percentage of the targeted young adults who will purchase the new game by allowing the same level of margin of error?

The width of a confidence interval equals twice the sampling error.

The t distribution

SCENARIO 8-9 A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students.A survey 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, a 99% confidence interval will contain 99% of the student population who feel comfortable reporting cheating by their fellow students.

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

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, it is possible that the 99% confidence interval calculated from the data will not contain the sample mean number of rooms rented daily in a given month.