Exam 8: Confidence Interval Estimation

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.

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 critical value for a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report is .

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

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,this interval requires the assumption that the distribution of the number of people recognizing the product has a normal distribution.

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 sample means will fall between 47.19 and 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 8-8 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,a 99% confidence interval for the proportion of the student population who own a personal computer is from _____to_____ .

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 the mean numbers of student population who own a personal computer is between 0.7911 and 0.8769.

Suppose a 95% confidence interval for has been constructed.If it is decided to take a larger sample and to decrease the confidence level of the interval,then the resulting interval width would_____ .(Assume that the sample statistics gathered would not change very much for the new sample. )

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

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,a 95% confidence interval for the mean number of rooms rented daily in a given month is narrower than a 99% confidence interval.

Given a sample mean of 2.1 and a population standard deviation of 0.7 from a sample of 10 data points,a 90% confidence interval will have a width of 2.36.

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,a 95% confidence interval for the proportion of the student population who own a personal computer is narrower than a 99% confidence interval.

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,we are 99% confident that between 45.57% and 50.43% of the student population feel comfortable reporting cheating by their fellow students.

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,it is possible that the mean of the population is not between 47.19 and 52.61.

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 for the proportion of the student population who feel comfortable reporting cheating by their fellow students is from_____ to_____ .

Which of the following is not true about the Student's t distribution?

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.

The county clerk wants to estimate the proportion of voters who will need special election facilities.Suppose a sample of 400 voters was taken.If 150 need special election facilities,calculate a 90% confidence interval for the population proportion.

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,this confidence interval is only valid if the scores on the Fortunato test are normally distributed.