Exam 8: Confidence Interval Estimation

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,what is the needed sample size to obtain a 95% confidence interval in estimating the percentage of the targeted young adults who will purchase the new game to within ±5% if you do not have the information on the 49% in the interviews who said that they would purchase the new game?

The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day.The assistant provides the following interval estimate: from 740 to 920 books per day.If the head librarian knows that the population standard deviation is 150 books checked out per day,and she asked her assistant to use 25 days of data to construct the interval estimate,what confidence level can she attach to the interval estimate?

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 indicates that the machine is not working properly.

When determining the sample size necessary for estimating the true population mean,which factor is not considered when sampling with replacement?

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,they should sample ________ employees if they want to estimate the mean score of the employees within 5 points with 90% confidence.

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,the critical value for a 99% confidence interval for this sample is ________.

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,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.

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

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

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,construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople working a second job on company time.

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.

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,a confidence interval estimate of the population mean would only be valid if the distribution of voltages is normal.

A random sample of 50 provides a sample mean of 31 with a standard deviation of S = 14.The upper bound of a 90% confidence interval estimate of the population mean is 34.32.

The width of a confidence interval estimate for a proportion will be

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 critical value used in constructing a 90% confidence interval is ________.

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

A major department store chain is interested in estimating the mean amount its credit card customers spent on their first visit to the chain's new store in the mall.Fifteen credit card accounts were randomly sampled and analyzed with the following results: X = $50.50 and S = 20.Construct a 95% confidence interval for the mean amount its credit card customers spent on their first visit to the chain's new store in the mall assuming that the amount spent follows a normal distribution.

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 = 19.8 and S = 5.Which of the following assumptions is necessary in order for a confidence interval to be valid?

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,what is the critical value for the 90% one-sided confidence interval for the proportion of students who had cheated on an exam during the last 12 months?

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 99% confidence interval will contain 99% of the sample mean number of rooms rented daily in a given month.