Exam 8: Confidence Interval Estimation

True or False: The difference between the sample size and the population size is called the sampling error.

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. -True or False: Referring to Table 8-4,a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

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,we are 99% confident that the total number of the student population who feel comfortable reporting cheating by their fellow students is between 0.4557 and 0.5043.

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,it is possible that the 99% confidence interval calculated from the data will not contain the population mean number of rooms rented daily in a given month.

True or False: For a given data set,the confidence interval will be wider for 95% confidence than for 90% confidence.

True or False: A point estimate consists of a single sample statistic that is used to estimate the true population parameter.

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 ________.

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

A confidence interval was used to estimate the proportion of statistics students who are females.A random sample of 72 statistics students generated the following 90% confidence interval: (0.438,0.642).Based on the interval above,is the population proportion of females equal to 0.60?

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. -The head of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option.A preliminary sample indicates that the proportion will be around 0.25.Therefore,what size sample should the department head take if she wants to be 95% confident that the estimate is within 0.10 of the true proportion?

True or False: 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 8-6 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 8-6,95% of the people will recognize the product between 36% and 54% of the time.

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. -True or False: Referring to Table 8-10,a 95% confidence interval will contain 95% of the population proportion of managers who have caught salespeople cheating on an expense report.

A quality control engineer is interested in estimating the proportion of defective items coming off a production line.In a sample of 300 items,27 are defective.A 90% confidence interval for the proportion of defectives from this production line would go from ________ to ________.

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 goes from ________ to ________.

True or False: A population parameter is used to estimate a confidence interval.

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. -True or False: Referring to Table 8-10,it is possible that the 95% confidence interval calculated from the data will not contain the sample proportion of managers who have caught salespeople cheating on an expense report.

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. -True or False: Referring to Table 8-5,95% of the time,the sample mean salary offer to management majors will fall between 47.19 and 52.61.

True or False: 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.

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,we are 99% confident that between 79.11% and 87.69% of the student population own a personal computer.