Exam 8: Confidence Interval Estimation

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 between 47.19 and 52.61.

Holding the width of a confidence interval fixed,increasing the level of confidence can be achieved with a lower sample size.

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,the sampling error of a 99% confidence interval for the mean number of rooms rented daily in a given month is ________.

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

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

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 8-6,95% of the time,the proportion of people that recognize the product will fall between 0.36 and 0.54.

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,it is possible that the 99% confidence interval calculated from the data will not contain the mean voltage for the sample.

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

TABLE 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 Table 8-2,the confidence interval is valid only if the lengths cut are normally distributed.

TABLE 8-11 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 Table 8-11,a 99% confidence interval will contain 99% of the student population who feel comfortable reporting cheating by their fellow students.

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,we are 99% confident that the average number of rooms rented daily in a given month is somewhere between 24.64 and 49.36.

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,for the confidence interval to be valid,it is necessary that test scores of students in the special study program on the actuarial exam be normally distributed.

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 superintendent can be 85% confident that no more than 1% of the students at the university had cheated on an exam during the last semester.

TABLE 8-11 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 Table 8-11,a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

A confidence interval was used to estimate the proportion of statistics students who are female.A random sample of 72 statistics students generated the following 90% confidence interval: (0.438,0.642).Using the information above,what total size sample would be necessary if we wanted to estimate the true proportion to within ±0.08 using 95% confidence?

TABLE 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 Table 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 ________.