Exam 8: Confidence Interval Estimation

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_____ .

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.

The sample mean is a point estimate of the population mean.

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 time,the proportion of people that recognize the product will fall between 0.36 and 0.54.

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 $\pi$ is 0.59 $\pm$ 0.07.Interpret this interval.

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 confidence interval is valid only if the lengths cut are normally distributed.

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 time,the sample mean salary offer to management majors will fall between 47.19 and 52.61.

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,determine the sample size needed to estimate the proportion of managers who have caught salespeople working a second job on company time to within ±0.02 with 95% confidence.

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 time,the sample proportion of people that recognize the product will fall between 0.36 and 0.54.

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 parameter of interest is the proportion of the rooms rented daily in a given month.

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 sampling error of a 99% confidence interval for the proportion of the student population who own a personal computer is .

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.

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, x? = 396 and S = 100.Estimate the mean number of admissions per 24-hour period with a 95% confidence interval.

A 99% confidence interval estimate can be interpreted to mean that

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 report contains all the essential components for an ethical reporting of poll results.

When determining the sample size for a proportion for a given level of confidence and sampling error,the closer to 0.50 that is estimated to be,the sample size required_____ .

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

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,the parameter of interest is the total number of students in the population who feel comfortable reporting cheating by their fellow students.

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

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.