Exam 8: Confidence Interval Estimation

TABLE 8-13 A sales and marketing management magazine conducted a survey of salespeople cheating on their expense reports and other unethical conduct.In the survey of 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 Table 8-13,we are 95% confident that the population mean number of managers who have caught salespeople cheating on an expense report is between 0.5116 to 0.6484.

TABLE 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 Table 8-6,this interval requires the use of the t distribution to obtain the confidence coefficient.

The sampling error can either be positive or negative.

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

TABLE 8-14 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 Table 8-14,1,500 is the size of the

TABLE 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 Table 8-3,the mean of the sample is ________,while the standard deviation of the sample is ________.

TABLE 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 Table 8-5,the confidence interval obtained is valid only if the distribution of the population of salary offers is normal.

TABLE 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 Table 8-5,it is possible that the mean of the population is not between 47.19 and 52.61.

TABLE 8-10 The president of a university is concerned that illicit drug use on campus is higher than the 5% targeted level.A random sample of 250 students from a population of 2,000 revealed that 7 of them had used illicit drugs during the last 12 months. -Referring to Table 8-10,the president can be 90% confident that no more than 5% of the students at the university had used illicit drugs during the last 12 months.

TABLE 8-10 The president of a university is concerned that illicit drug use on campus is higher than the 5% targeted level.A random sample of 250 students from a population of 2,000 revealed that 7 of them had used illicit drugs during the last 12 months. -Referring to Table 8-10,what is the upper bound of the 90% one-sided confidence interval for the proportion of students who had used illicit drugs during the last 12 months?

Suppose a department store wants to estimate the mean age of the customers of its contemporary apparel department,correct to within 2 years,with level of confidence equal to 95%.Management believes that the standard deviation is 8 years.The sample size they should take is ________.

TABLE 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 Table 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 ________.

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.

TABLE 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 Table 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.

TABLE 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 Table 8-4,the critical value for a 99% confidence interval for this sample is ________.

TABLE 8-12 The president of a university is concerned that the percentage of students who have cheated on an exam is higher than the 1% acceptable level.A confidential random sample of 1,000 students from a population of 7,000 revealed that 6 of them said that they had cheated on an exam during the last semester. -Referring to Table 8-12,using the 90% one-sided confidence interval,the president can be 95% confident that no more than 1% of the students at the university had cheated on an exam during the last semester.

TABLE 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 Table 8-8,the sampling error of a 99% confidence interval for the proportion of the student population who own a personal computer is ________.

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?

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.

TABLE 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 24 rooms.During February,a sample of 25 days has a sample mean of 37 rooms. -Referring to Table 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.