Exam 8: Confidence Interval Estimation

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

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 report contains all the essential components for an ethical reporting of poll results.

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." -Referring to Table 8-9,the critical value for a 99% confidence interval for this sample is ________.

True or False: The difference between the upper limit of a confidence interval and the point estimate used in constructing the confidence interval is called the sampling error.

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

Suppose a 95% confidence interval for μ has been constructed.If it is decided to take a larger sample and to decrease the confidence level of the interval,then the resulting interval width would ________.(Assume that the sample statistics gathered would not change very much for the new sample.)

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 95% confidence interval for the mean voltage of the power pack is wider than a 99% confidence interval.

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.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.

TABLE 8-12 A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results. -True or False: Referring to Table 8-12,the confidence interval estimate of the mean with finite population correction will be wider in range than confidence interval estimate without finite population correction.

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

Suppose a department store wants to estimate the mean age of the customers of its contemporary apparel department,correct to within 2 years,with level of confidence equal to 95%.Management believes that the standard deviation is 8 years.The sample size they should take is ________.

A university dean is interested in determining the proportion of students who receive some sort of financial aid.Rather than examine the records for all students,the dean randomly selects 200 students and finds that 118 of them are receiving financial aid.If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability,how many students would need to be sampled?

Suppose a 95% confidence interval for μ turns out to be (1,000,2,100).To make more useful inferences from the data,it is desired to reduce the width of the confidence interval.Which of the following will result in a reduced interval width?

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 sample means will fall between 47.19 and 52.61.

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,determine the sample size needed to estimate the proportion of managers who have caught salespeople working a second job on company time to within ±0.02 with 95% confidence.

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 working a second job on company time is ________.

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 sample proportion of students 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 240 rooms.During February,a sample of 25 days has a sample mean of 370 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 ________.

TABLE 8-12 A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results. -True or False: Referring to Table 8-12,95% of the stores have sold between 5.623 and 6.377 lawnmowers.