Exam 8: Confidence Interval Estimation

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 confidence interval will be based on ________ degrees of freedom.

TABLE 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 Table 8-10,the sampling error of a 95% confidence interval estimate of the population proportion of managers who have caught salespeople giving a kickback to a customer is ________.

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. -True or False: Referring to Table 8-8,the parameter of interest is the proportion of the student population who own a personal computer.

TABLE 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. -True or False: Referring to Table 8-11,the size of the population is 1,500.

Suppose a 95% confidence interval for μ turns out to be (1,000,2,100).Give a definition of what it means to be "95% confident" as an inference.

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

True or False: Other things being equal,as the confidence level for a confidence interval increases,the width of the interval increases.

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. -True or False: Referring to Table 8-6,the parameter of interest to the manager is the proportion of potential customers in this sample that recognize the new product.

TABLE 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 Table 8-10,construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople listing a "strip bar" as a restaurant on an expense report.

TABLE 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 Table 8-10,construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople working a second job on company time.

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: = $50.50 and S = 20.Assuming the distribution of the amount spent on their first visit is normal,what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for μ?

TABLE 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 Table 8-11,what is the needed sample size to obtain a 95% confidence interval estimate of the percentage of the targeted young adults who will purchase the new game by allowing the same level of margin of error?

True or False: Other things being equal,the confidence interval for the mean will be wider for 95% confidence than for 90% confidence.

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 240 rooms.During February,a sample of 25 days has a sample mean of 370 rooms. -True or False: Referring to Table 8-7,the parameter of interest is the proportion of the rooms rented daily in a given month.

True or False: 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.

TABLE 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." -True or False: Referring to Table 8-9,it is possible that the 99% confidence interval calculated from the data will not contain the proportion of the student population who feel comfortable reporting cheating by their fellow students.

True or False: The t distribution allows the calculation of confidence intervals for means when the actual standard deviation is not known.

TABLE 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 Table 8-11,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%?

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. -True or False: Referring to Table 8-6,this interval requires the use of the t distribution to obtain the confidence coefficient.

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,a 99% confidence interval for the proportion of the student population who own a personal computer is from ________ to ________.