Deck 8: Confidence Interval Estimation

Question 1

When determining the sample size for a proportion for a given level of confidence and sampling error, the closer to 0.50 that u is estimated to be, the sample size required

A) is smaller.
B) can be smaller, larger or unaffected.
C) is larger.
D) is not affected.

Answer 1

C

Question 2

It is desired to estimate the average total compensation of CEOs in the Service industry. Data were randomly collected from 18 CEOs and the 97% confidence interval was calculated to be ($2,181,260, $5,836,180). Which of the following interpretations is correct?

A) In the population of Service industry CEOs, 97% of them will have total compensations that fall in the interval $2,181,260 to $5,836,180.
B) We are 97% confident that the average total compensation of all CEOs in the Service industry falls in the interval $2,181,260 to $5,836,180.
C) We are 97% confident that the mean of the sampled CEOs falls in the interval $2,181,260 to $5,836,180.
D) 97% of the sampled total compensation values fell between $2,181,260 and $5,836,180.

Answer 2

B

Question 3

In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a_____ interval.

A) less significant
B) biased
C) wider
D) narrower

Answer 3

narrower

Question 4

An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the width of the 90% confidence interval?

A) $364.30
B) $728.60
C) $232.60
D) $465.23

Question 5

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?

A) 95.4%
B) 99.7%
C) 98.0%
D) 99.0%

Question 6

The t distribution

A) approaches the normal distribution as the sample size increases.
B) assumes the population is normally distributed.
C) has more area in the tails than does the normal distribution.
D) all of the above

Question 7

A 99% confidence interval estimate can be interpreted to mean that

A) if all possible samples are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval.
B) we have 99% confidence that we have selected a sample whose interval does include the population mean.
C) both of the above
D) none of the above

Question 8

An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the upper end point in a 99% confidence interval for the average income?

A) $15,141
B) $15,364
C) $15,052
D) $15,330

Question 9

Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. Summary statistics yield $\overline{ X }= 180.975$ and s = 143.042. Calculate a 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments.

A) $180.975 ± $116.621
B) $180.975 ± $94.066
C) $180.975 ± $119.586
D) $180.975 ± $99.123

Question 10

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, $\overline{X }= 19.8$ and s² = 25. Which of the following assumptions is necessary in order for a confidence interval to be valid?

A) The population sampled from has an approximate t distribution.
B) The mean of the sample equals the mean of the population.
C) The population sampled from has an approximate normal distribution.
D) None of these assumptions are necessary.

Question 11

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

A) It has more area in the tails and less in the center than does the normal distribution.
B) It is bell shaped and symmetrical.
C) It is used to construct confidence intervals for the population mean when the population standard deviation is known.
D) As the number of degrees of freedom increases, the t distribution approaches the normal distribution.

Question 12

A major department store chain is interested in estimating the average 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 s2 = 400. Assuming the distribution of the amount spent on their first visit is approximately 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?

A) a t distribution with 14 degrees of freedom
B) a t distribution with 15 degrees of freedom
C) approximately normal with a mean of $50.50
D) a standard normal distribution

Question 13

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, approximately how large a sample did her assistant use to determine the interval estimate?

A) 3
B) 12
C) 2
D) It cannot be determined from the information given.

Question 14

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 be ____. (Assume that the sample statistics gathered would not change very much for the new sample.)

A) narrower than the current interval width
B) larger than the current interval width
C) the same as the current interval width
D) unknown until actual sample sizes and reliability levels were determined

Question 15

A major department store chain is interested in estimating the average 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: $\overline{X} = \$50.50$ and s² = 400. Construct a 95% confidence interval for the average 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.

A) $50.50 ± $11.00
B) $50.50 ± $9.09
C) $50.50 ± $10.12
D) $50.50 ± $11.08

Question 16

An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What total sample size would the economist need to use for a 95% confidence interval if the width of the interval should not be more than $100?

A) n = 385
B) n = 1537
C) n = 40
D) n = 20

Question 17

If you were constructing a 99% confidence interval of the population mean based on a sample of n=25 where the standard deviation of the sample s = 0.05, what will be the critical value of t?

A) 2.7969
B) 2.7874
C) 2.4851
D) 2.4922

Question 18

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

A) wider for a sample size of 100 than for a sample size of 50.
B) narrower when the sample proportion is 0.50 than when the sample proportion is 0.20.
C) narrower for 90% confidence than for 95% confidence.
D) narrower for 99% confidence than for 95% confidence.

Question 19

It is desired to estimate the average total compensation of CEOs in the Service industry. Data were randomly collected from 18 CEOs and the 97% confidence interval was calculated to be ($2,181,260, $5,836,180). Based on the interval above, do you believe the average total compensation of CEOs in the Service industry is more than $3,000,000?

A) I am 97% confident that the average compensation is $3,000,000.
B) I cannot conclude that the average exceeds $3,000,000 at the 97% confidence level.
C) Yes, and I am 97% confident of it.
D) Yes, and I am 78% confident of it.

Question 20

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. What is an efficient, unbiased point estimate of the number of books checked out each day at the Library of Congress?

A) 1,660
B) 920
C) 740
D) 830

Question 21

TABLE 8-15
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, managers have caught salespeople cheating on an expense report 58% of the time, working a second job on company time 50% of the time, listing a "strip bar" as a restaurant on an expense report 22% of the time, and giving a kickback to a customer 19% of the time.

-Referring to Table 8-15, 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.

Question 22

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. The 95% confidence interval for p is 1. ± 0.07. Interpret this interval.

A) 95% of the students get between 52% and 66% of their tuition paid for by financial aid.
B) We are 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66.
C) We are 95% confident that 59% of the students are on some sort of financial aid.
D) We are 95% confident that between 52% and 66% of the sampled students receive some sort of financial aid.

Question 23

TABLE 8-10
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 8-10, a 99% confidence interval for the proportion of student population who own a personal computer is from _____ to _____.

Question 24

TABLE 8-8
A hotel chain wants to estimate the average number of rooms rented daily in each month. The population of rooms rented daily is assumed to be normally distributed for each month with a standard deviation of 24 rooms.

-Referring to Table 8-8, during February, a sample of 25 days has a sample mean of 37 rooms. Use this information to calculate a 92% confidence interval for the population mean.

Question 25

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.

A) 95% of the observations in the entire population fall in the given interval.
B) In repeated sampling, the population parameter would fall in the given interval 95% of the time.
C) 95% of the observations in the sample fall in the given interval.
D) In repeated sampling, 95% of the intervals constructed would contain the population mean.

Question 26

TABLE 8-2
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 8-2, 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 _____ .

Question 27

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?

A) n = 1,435
B) n = 1,503
C) n = 1,784
D) n = 1,844

Question 28

TABLE 8-2
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 8-2, they should sample____ employees if they want to estimate the mean score of the employees within 5 points with 90% confidence.

Question 29

A confidence interval was used to estimate the proportion of statistics students that 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 ±0.08 using 95% confidence?

A) 105
B) 597
C) 150
D) 420

Question 30

TABLE 8-9
A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburban county in Chicago. His main concern is the total market value of the 3,605 houses in the suburban county. He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample average market price of
$225,000 and a sample standard deviation of $38,700. The consulting group also found out that the average differences between market prices and appraised prices was $125,000 with a standard deviation of $3,400. Also the proportion of houses in the sample that are appraised for higher than the market prices is 0.24.

-Referring to Table 8-9, what will be the 90% confidence interval for the average market price of the houses in the suburban county constructed by the consulting group?

Question 31

Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. What value will be used as the point estimate for the mean endowment of all private colleges in the United States?

A) $1,447.8
B) $143.042
C) $8
D) $180.975

Question 32

A prison official wants to estimate the proportion of cases of recidivism. Examining the records of 250 convicts, the official determines that there are 65 cases of recidivism. A 99% confidence interval for the proportion of cases of recidivism would go from_________ to_______
.

Question 33

A confidence interval was used to estimate the proportion of statistics students that 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?

A) Maybe. 0.60 is a believable value of the population proportion based on the information above.
B) Yes, and we are 90% sure of it.
C) No, and we are 90% sure of it.
D) No. The proportion is 54.17%.

Question 34

TABLE 8-13
A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students. A surveyed 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 8-13, a 99% confidence interval for the proportion of student population who feel comfortable reporting cheating by their fellow students is from____ to____

Question 35

TABLE 8-11
The superintendent of a unified school district of a small town wants to make sure that no more than 5% of the students skip more than 10 days of school in a year. A random sample of 145 students from a population of 800 showed that 12 students skipped more than 10 days of school last year.
Referring to Table 8-11, what is the upper bound of the 95% one-sided confidence interval for the proportion of students who skipped more than 10 days of school last year?

Question 36

TABLE 8-15
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, managers have caught salespeople cheating on an expense report 58% of the time, working a second job on company time 50% of the time, listing a "strip bar" as a restaurant on an expense report 22% of the time, and giving a kickback to a customer 19% of the time.

-Referring to Table 8-15, the sampling error of a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report is ______.

Question 37

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 for a 95% confidence interval, approximately how large a sample did her assistant use to determine the interval estimate?

A) 13
B) 4
C) 125
D) 11

Question 38

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

A) the population standard deviation
B) the allowable or tolerable sampling error
C) the level of confidence desired in the estimate
D) the population size

Question 39

TABLE 8-5
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 8-5, a 99% confidence interval for the mean voltage of the power packs is from ____ to_____ .

Question 40

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?

A) increase the sample size
B) increase the sample mean
C) increase the population mean
D) increase the confidence level

Question 41

TABLE 8-15
A sales and marketingmanagement magazine conducted a surveyonsalespeople cheatingon their expense reports and other unethicalconduct. In thesurvey on 200 managers, managers have caughtsalespeople cheatingonanexpense report $58 \%$ of the time, workinga second job oncompany time $50 \%$ of the time, listinga "strip bar" as a restauranton anexpense report $22 \%$ of the time, and givinga kickback to a customer $19 \%$ of the time.

-Referring to Table 8-15, 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.

Question 42

TABLE 8-10
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 8-10, the critical value for a 99% confidence interval for this sample is______

Question 43

TABLE 8-5
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 8-5, a confidence interval for this sample would be based on the t
distribution with _______ degrees of freedom.

Question 44

TABLE 8-15
A sales and marketingmanagement magazine conducted a surveyonsalespeople cheatingon their expense reports and other unethicalconduct. In thesurvey on 200 managers, managers have caughtsalespeople cheatingonanexpense report $58 \%$ of the time, workinga second job oncompany time $50 \%$ of the time, listinga "strip bar" as a restauranton anexpense report $22 \%$ of the time, and givinga kickback to a customer $19 \%$ of the time.

-Referring to Table 8-15, the critical value for a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report is______ .

Question 45

The county clerk wants to estimate the proportion of retired voters who will need special election facilities. Suppose a sample of 400 retired voters was taken. If 150 need special election facilities, calculate an 80% confidence interval for the population proportion.

Question 46

TABLE 8-11
The superintendent of a unified school district of a small town wants to make sure that no more than 5% of the students skip more than 10 days of school in a year. A random sample of 145 students from a population of 800 showed that 12 students skipped more than 10 days of school last year.
Referring to Table 8-11, what is the critical value for the 95% one-sided confidence interval for the proportion of students who skipped more than 10 days of school last year?

Question 47

TABLE 8-5
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 8-5, the critical value for a 99% confidence interval for this sample is______

Question 48

TABLE 8-4
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 8-4, the confidence interval will be based on_____ degrees of freedom.

Question 49

A prison official wants to estimate the proportion of cases of recidivism. Examining the records of 250 convicts, the official determines that there are 65 cases of recidivism. A confidence interval will be obtained for the proportion of cases of recidivism. Part of this calculation includes the estimated standard error of the sample proportion. For this sample, the estimated standard error is _____ .

Question 50

The county clerk wants to estimate the proportion of retired voters who will need special election facilities. The clerk wants to find a 95% confidence interval for the population proportion which extends at most 0.07 to either side of the sample proportion. How large a sample must be taken to assure these conditions are met?

Question 51

TABLE 8-15
A sales and marketingmanagement magazine conducted a surveyonsalespeople cheatingon their expense reports and other unethicalconduct. In thesurvey on 200 managers, managers have caughtsalespeople cheatingonanexpense report $58 \%$ of the time, workinga second job oncompany time $50 \%$ of the time, listinga "strip bar" as a restauranton anexpense report $22 \%$ of the time, and givinga kickback to a customer $19 \%$ of the time.

-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, $\overline{X}$ = 19.8 and s² = 25. Estimate the mean number of admissions per 24-hour period with a 95% confidence interval.

Question 52

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?

Question 53

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. Use a 90% confidence interval to estimate the true proportion of students who receive financial aid.

Question 54

TABLE 8-12
The president of a university is concerned that illicit drug use on campus is higher than the 5% acceptable level. A random sample of 250 students from a population of 2000 revealed that 7 of them had used illicit drug during the last 12 months.
Referring to Table 8-12, what is the critical value for the 90% one-sided confidence interval for the proportion of students who had used illicit drug during the last 12 months?

Question 55

TABLE 8-4
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 8-4, the critical value used in constructing a 90% confidence interval is____

Question 56

TABLE 8-3
A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired 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 8-3, the critical value to use in obtaining the confidence interval is______

Question 57

TABLE 8-15
A sales and marketingmanagement magazine conducted a surveyonsalespeople cheatingon their expense reports and other unethicalconduct. In thesurvey on 200 managers, managers have caughtsalespeople cheatingonanexpense report $58 \%$ of the time, workinga second job oncompany time $50 \%$ of the time, listinga "strip bar" as a restauranton anexpense report $22 \%$ of the time, and givinga kickback to a customer $19 \%$ of the time.

-Referring to Table 8-15, construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report

Question 58

TABLE 8-14
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 1000 students from a population of 7000 revealed that 6 of them said that they had cheated on an exam during the last semester.
Referring to Table 8-14, 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?

Question 59

A university system enrolling hundreds of thousands of students is considering a change in the way students pay for their education. Currently, the students pay $55 per credit hour. The university system administrators are contemplating charging each student a set fee of $750 per quarter, regardless of how many credit hours each takes. To see if this proposal would be economically feasible, the administrators would like to know how many credit hours, on the average, each student takes per quarter. A random sample of 250 students yields a mean of 14.1 credit hours per quarter and a standard deviation of 2.3 credit hours per quarter. Suppose the administration wanted to estimate the mean to within 0.1 hours at 95% reliability and assumed that the sample standard deviation provided a good estimate for the population standard deviation. How large a total sample would they need to take?

Question 60

TABLE 8-13
A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students. A surveyed 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 8-13, the critical value for a 99% confidence interval for this sample is_____
.

Question 61

TABLE 8-9
A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburban county in Chicago. His main concern is the total market value of the 3,605 houses in the suburban county. He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample average market price of
$225,000 and a sample standard deviation of $38,700. The consulting group also found out that the average differences between market prices and appraised prices was $125,000 with a standard deviation of $3,400. Also the proportion of houses in the sample that are appraised for higher than the market prices is 0.24.

-Referring to Table 8-9, what will be the 90% confidence interval for the total difference between the market prices and appraised prices of the houses in the suburban county constructed by the consulting group?

Question 62

TABLE 8-14
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 1000 students from a population of 7000 revealed that 6 of them said that they had cheated on an exam during the last semester.
Referring to Table 8-14, what is the upper bound of the 90% one-sided confidence interval for the proportion of students who had cheated on an exam during the last 12 months?

Question 63

TABLE 8-9
A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburban county in Chicago. His main concern is the total market value of the 3,605 houses in the suburban county. He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample average market price of
$225,000 and a sample standard deviation of $38,700. The consulting group also found out that the average differences between market prices and appraised prices was $125,000 with a standard deviation of $3,400. Also the proportion of houses in the sample that are appraised for higher than the market prices is 0.24.
Referring to Table 8-9, what will be the 90% confidence interval for the population proportion of houses that will be appraised for higher than the market prices?

Question 64

TABLE 8-4
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 8-4, a 90% confidence interval for the mean score of actuarial students in the special program is from _____to_____.

Question 65

TABLE 8-3
A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired 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 8-3, suppose the engineer had decided to estimate the mean length to within 0.03 with 99% confidence. Then the sample size would be _____.

Question 66

TABLE 8-9
A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburban county in Chicago. His main concern is the total market value of the 3,605 houses in the suburban county. He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample average market price of
$225,000 and a sample standard deviation of $38,700. The consulting group also found out that the average differences between market prices and appraised prices was $125,000 with a standard deviation of $3,400. Also the proportion of houses in the sample that are appraised for higher than the market prices is 0.24.
Referring to Table 8-9, what will be the 90% confidence interval for the total market price of the houses in the suburban county constructed by the consulting group?

Question 67

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. Suppose there is no information about the proportion of students who might choose the option. 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?

Question 68

TABLE 8-12
The president of a university is concerned that illicit drug use on campus is higher than the 5% acceptable level. A random sample of 250 students from a population of 2000 revealed that 7 of them had used illicit drug during the last 12 months.
Referring to Table 8-12, what is the upper bound of the 90% one-sided confidence interval for the proportion of students who had used illicit drug during the last 12 months?

Question 69

TABLE 8-3
A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired 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 8-3, the confidence interval goes from____ to____ .

Question 70

TABLE 8-8
A hotel chain wants to estimate the average number of rooms rented daily in each month. The population of rooms rented daily is assumed to be normally distributed for each month with a standard deviation of 24 rooms.
Referring to Table 8-8, during January, a sample of 16 days has a sample mean of 48 rooms. This information is used to calculate an interval estimate for the population mean to be from 40 to 56 rooms. What is the level of confidence of this interval?

Question 71

TABLE 8-15
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, managers have caught salespeople cheating on an expense report 58% of the time, working a second job on company time 50% of the time, listing a "strip bar" as a restaurant on an expense report 22% of the time, and giving a kickback to a customer 19% of the time.

-Referring to Table 8-15, 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______ .

Question 72

TABLE 8-15
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, managers have caught salespeople cheating on an expense report 58% of the time, working a second job on company time 50% of the time, listing a "strip bar" as a restaurant on an expense report 22% of the time, and giving a kickback to a customer 19% of the time.
Referring to Table 8-15, construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople working a second job on company time.

Question 73

TABLE 8-15
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, managers have caught salespeople cheating on an expense report 58% of the time, working a second job on company time 50% of the time, listing a "strip bar" as a restaurant on an expense report 22% of the time, and giving a kickback to a customer 19% of the time.
Referring to Table 8-15, construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople giving a kickback to a customer.

Question 74

TABLE 8-13
A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students. A surveyed 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 8-13, the sampling error of a 99% confidence interval for the proportion of student population who feel comfortable reporting cheating by their fellow students is______

Question 75

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, $\overline{X}$ = 19.8 and s² = 25. Using the sample standard deviation as an estimate for the population standard deviation, what size sample should the director choose if she wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 99% reliability?

Question 76

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____ .

Question 77

$$\text { TABLE 8-10 }$$ 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 8-10, the sampling error of a 99% confidence interval for the proportion of student population who own a personal computer is_____ .

Question 78

TABLE 8-4
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 8-4, the mean of the sample is____ , while the standard deviation of the sample is _____.

Question 79

Suppose a department store wants to estimate the average 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 ____.

Question 80

TABLE 8-9
A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburban county in Chicago. His main concern is the total market value of the 3,605 houses in the suburban county. He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample average market price of
$225,000 and a sample standard deviation of $38,700. The consulting group also found out that the average differences between market prices and appraised prices was $125,000 with a standard deviation of $3,400. Also the proportion of houses in the sample that are appraised for higher than the market prices is 0.24.
Referring to Table 8-9, if he wants a 95% confidence on estimating the true population average market price of the houses in the suburban county to be within $10,000, how large a sample will he need?