Exam 8: Confidence Interval Estimation

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 if the amount spent follows a normal distribution.

SCENARIO 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 Scenario 8-8,it is possible that the 99% confidence interval calculated from the data will not contain the sample proportion of students who own a personal computer.

SCENARIO 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 Scenario 8-5,95% of all confidence intervals constructed similarly to this one with a sample size of 10 will contain the mean of the population.

SCENARIO 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 Scenario 8-10,the sampling error of 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 is .

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

SCENARIO 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 Scenario 8-4,a confidence interval estimate of the population mean would only be valid if the distribution of voltages is normal.

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?

SCENARIO 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 Scenario 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 .

SCENARIO 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 Scenario 8-4,the critical value for a 99% confidence interval for this sample is .

SCENARIO 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 Scenario 8-2,the critical value to use in obtaining the confidence interval is .

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 $\pm$ 0.08 using 95% confidence?

SCENARIO 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". -Referring to Scenario 8-9,a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

SCENARIO 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. -Referring to Scenario 8-7,a 99% confidence interval will contain 99% of the sample mean number of rooms rented daily in a given month.

SCENARIO 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 Scenario 8-8,a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

SCENARIO 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 Scenario 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.

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.

SCENARIO 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 Scenario 8-10,we are 95% confident that between 51.16% and 64.84% of managers in the population have caught salespeople cheating on an expense report.

SCENARIO 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. -Referring to Scenario 8-7,we are 99% confident that the average number of rooms rented daily in a given month is somewhere between 246.36 and 493.64.

SCENARIO 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 Scenario 8-4,a 95% confidence interval for the mean voltage of the power pack is wider than a 99% confidence interval.

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