# Chapter 07 Sample New Models Automobiles Provides The Following

Document Type

Test Prep

Book Title

Essentials of Modern Business Statistics 4th (Fourth) Edition By Williams 4th Edition

Authors

J.K

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b. the same as convenience sampling

c. a probability sampling method

d. None of the alternative answers is correct.

86. Convenience sampling is an example of

a. probabilistic sampling

b. stratified sampling

c. a nonprobability sampling technique

d. cluster sampling

87. Which of the following is an example of a nonprobability sampling technique?

a. simple random sampling

b. stratified random sampling

c. cluster sampling

d. judgment sampling

88. Which of the following sampling methods does not lead to probability samples?

a. stratified sampling

b. cluster sampling

c. systematic sampling

d. convenience sampling

89. The population we want to make inferences about is the

a. sampled population

b. frame

c. target population

d. finite population

PROBLEMS

1. A simple random sample of 8 employees of a corporation provided the following

information.

Employee

1

2

3

4

5

6

7

8

Age

25

32

26

40

50

54

22

23

Gender

M

M

M

M

F

M

M

F

a. Determine the point estimate for the average age of all employees.

b. What is the point estimate for the standard deviation of the population?

c. Determine a point estimate for the proportion of all employees who are female.

2. Starting salaries of a sample of five management majors along with their genders are

shown below.

Employee

Salary ($1000s)

Gender

1

30

F

2

28

M

3

22

F

4

26

F

5

19

M

a. What is the point estimate for the starting salaries of all management majors?

b. Determine the point estimate for the variance of the population.

c. Determine the point estimate for the proportion of male employees.

3. A sample of 8 new models of automobiles provides the following data on highway miles

per gallon. Use Excel to answer the questions that follow the data.

Model

Highway Miles

Per Gallon

1

33.6

2

26.8

3

20.2

4

38.7

5

35.1

6

28.0

7

26.2

8

27.6

a. What is the point estimate for the average highway miles per gallon for all new

models of autos?

b. Determine the point estimate for the standard deviation of the population.

4. A sample of 10 members of a video club provides the following data on number of videos

they own. Use Excel to answer the questions that follow the data.

Member

Number Owned

1

200

2

26

3

158

4

75

5

52

6

352

7

17

8

276

9

488

10

129

a. What is the point estimate for the mean number of videos owned by all video

club members?

b. Determine the point estimate for the standard deviation of the population.

5. Consider a population of five weights identical in appearance but weighing 1, 3, 5, 7, and

9 ounces.

a. Determine the mean and the variance of the population.

b. Sampling without replacement from the above population with a sample size of 2

produces ten possible samples. Using the ten sample mean values, determine the

mean of the population and the variance of

x

.

c. Compute the standard error of the mean.

6. Consider a population of five families with the following data representing the number of

pets in each family.

Family

Number of Pets

A

2

B

6

C

4

D

3

E

1

a. There are ten possible samples of size 2 (sampling without replacement). List the

10 possible samples of size 2, and determine the mean of each sample.

b. Determine the mean and the variance of the population.

c. Using the ten sample mean values, compute the mean and the standard error of the

mean.

7. The following information gives the number of days absent from work for a population of

5 workers at a small factory.

Worker

Number of

Days Absent

A

5

B

7

C

1

D

4

E

8

a. Find the mean and the standard deviation for the population.

b. Samples of size 2 will be drawn from the population. Use the answers in part a

to calculate the expected value and the standard deviation of the sampling

distribution of the sample mean.

c. Find all the samples of 2 workers that can be extracted from this population.

Choose the samples without replacement.

d. Compute the sample mean

x

for each of the samples in Part c.

e. Graph the sample means with the values of

x

on the horizontal axis and the

corresponding relative frequency on the vertical axis.

8. The average weekly earnings of bus drivers in a city are $950 (that is

) with a standard

deviation of $45 (that is

). Assume that we select a random sample of 81 bus drivers.

a. Assume the number of bus drivers in the city is large compared to the sample size.

Compute the standard error of the mean.

b. What is the probability that the sample mean will be greater than $960?

c. If the population of bus drivers consisted of 400 drivers, what would be the

standard error of the mean?

9. An automotive repair shop has determined that the average service time on an automobile

is 2 hours with a standard deviation of 32 minutes. A random sample of 64 services is

selected.

a. What is the probability that the sample of 64 will have a mean service time greater

than 114 minutes?

b. Assume the population consists of 400 services. Determine the standard error of

the mean.

10. A population of 1,000 students spends an average of $10.50 a day on dinner. The

standard deviation of the expenditure is $3. A simple random sample of 64 students is

taken.

a. What are the expected value, standard deviation, and shape of the sampling

distribution of the sample mean?

b. What is the probability that these 64 students will spend a combined total of more

than $715.21?

c. What is the probability that these 64 students will spend a combined total

between $703.59 and $728.45?

11. There are 8,000 students at the University of Tennessee at Chattanooga. The average age

of all the students is 24 years with a standard deviation of 9 years. A random sample of

36 students is selected.

a. Determine the standard error of the mean.

b. What is the probability that the sample mean will be larger than 19.5?

c. What is the probability that the sample mean will be between 25.5 and 27 years?

12. The life expectancy in the United States is 75 with a standard deviation of 7 years. A

random sample of 49 individuals is selected.

a. What is the probability that the sample mean will be larger than 77 years?

b. What is the probability that the sample mean will be less than 72.7 years?

c. What is the probability that the sample mean will be between 73.5 and 76 years?

d. What is the probability that the sample mean will be between 72 and 74 years?

e. What is the probability that the sample mean will be larger than 73.46 years?

13. SAT scores have an average of 1200 with a standard deviation of 60. A sample of 36

scores is selected.

a. What is the probability that the sample mean will be larger than 1224?

b. What is the probability that the sample mean will be less than 1230?

c. What is the probability that the sample mean will be between 1200 and 1214?

d. What is the probability that the sample mean will be greater than 1200?

e. What is the probability that the sample mean will be larger than 73.46?

14. A bank has kept records of the checking balances of its customers and determined that

the average daily balance of its customers is $300 with a standard deviation of $48. A

random sample of 144 checking accounts is selected.

a. What is the probability that the sample mean will be more than $306.60?

b. What is the probability that the sample mean will be less than $308?

c. What is the probability that the sample mean will be between $302 and $308?

d. What is the probability that the sample mean will be at least $296?

15. Students of a large university spend an average of $5 a day on lunch. The standard

deviation of the expenditure is $3. A simple random sample of 36 students is taken.

a. What are the expected value, standard deviation, and shape of the sampling

distribution of the sample mean?

b. What is the probability that the sample mean will be at least $4?

c. What is the probability that the sample mean will be at least $5.90?

16. The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours.

A simple random sample of 36 bulbs is taken.

a. What are the expected value, standard deviation, and shape of the sampling

distribution of

x

?

b. What is the random variable in this problem? Define it in words.

c. What is the probability that the average life in the sample will be between

2,670.56 and 2,809.76 hours?

d. What is the probability that the average life in the sample will be greater than

3,219.24 hours?

e. What is the probability that the average life in the sample will be less than

3,180.96 hours?

17. MNM Corporation gives each of its employees an aptitude test. The scores on the test

are normally distributed with a mean of 75 and a standard deviation of 15. A simple

random sample of 25 is taken from a population of 500.

a. What are the expected value, the standard deviation, and the shape of the

sampling distribution of

x

?

b. What is the random variable in this problem? Define it in words.

c. What is the probability that the average aptitude test score in the sample will be

between 70.14 and 82.14?

d. What is the probability that the average aptitude test score in the sample will be

greater than 82.68?

e. What is the probability that the average aptitude test score in the sample will be

less than 78.69?

f. Find a value, C, such that P(

x

C) = .015.

18. The price of a particular brand of jeans has a mean of $37.99 and a standard deviation of

$7. A sample of 49 pairs of jeans is selected. Use Excel to answer the following

questions.

a. What is the probability that the sample of jeans will have a mean price less than

$40?

b. What is the probability that the sample of jeans will have a mean price between

$38 and $39?

c. What is the probability that the sample of jeans will have a mean price within $3

of the population mean?

19. The mean diameter of a ball bearing produced by a certain manufacturer is 0.80 cm with

a standard deviation of 0.03 cm. A sample of 36 ball bearings is randomly selected from

a production run. Use Excel to answer the following questions.

a. What is the probability that the sample of ball bearings will have a mean less

than 0.798 cm?

b. What is the probability that the sample of ball bearings will have a mean of at

least 0.815 cm?

c. What is the probability that the sample of ball bearings will have a mean between

0.798 and 0.815 cm?

d. For samples of size 36, 15% of all sample means are at most what diameter?

20. There are 500 employees in a firm, 45% are female. A sample of 60 employees is

selected randomly.

a. Determine the standard error of the proportion.

b. What is the probability that the sample proportion of females is between 0.40 and

0.55?

21. Ten percent of the items produced by a machine are defective. A random sample of 100

items is selected and checked for defects.

a. Determine the standard error of the proportion.

b. What is the probability that the sample will contain more than 2.5% defective

units?

c. What is the probability that the sample will contain more than 13% defective

units?

22. A new soft drink is being market tested. It is estimated that 60% of consumers will like

the new drink. A sample of 96 taste-tested the new drink.

a. Determine the standard error of the proportion

b. What is the probability that more than 70.4% of consumers will indicate they like

the drink?

c. What is the probability that more than 30% of consumers will indicate they do not

like the drink?

23. In a large university, 20% of the students are business majors. A random sample of 100

students is selected, and their majors are recorded.

a. Compute the standard error of the proportion.

b. What is the probability that the sample contains at least 12 business majors?

c. What is the probability that the sample contains less than 15 business majors?

d. What is the probability that the sample contains between 12 and 14 business

majors?

24. In a local university, 10% of the students live in the dormitories. A random sample of

100 students is selected for a particular study.

a. What is the probability that the sample proportion of students living in the

dormitories is between 0.172 and 0.178?

b. What is the probability that the sample proportion of students living in the

dormitories is greater than 0.025?

25. A department store has determined that 25% of all their sales are credit sales. A random

sample of 75 sales is selected.

a What is the probability that the sample proportion will be greater than 0.34?

b. What is the probability that the sample proportion will be between 0.196 and

0.354?

c. What is the probability that the sample proportion will be less than 0.25?

d. What is the probability that the sample proportion will be less than 0.10?

26. Candidate A is running for president of the student government at a large university. The

proportion of voters who favor the candidate is 0.8. A simple random sample of 100

voters is taken.

a. What are the expected value, standard deviation, and shape of the sampling

distribution of

p

?

b. What is the probability that the number of voters in the sample who will not

favor Candidate A will be between 26 and 30?

c. What is the probability that the number of voters in the sample who will not

favor Candidate A will be more than 16?

27. In a restaurant, the proportion of people who order coffee with their dinner is 0.9. A

simple random sample of 144 patrons of the restaurant is taken.

a. What are the expected value, standard deviation, and shape of the sampling

distribution of

p

?

b. What is the random variable in this problem? Define it in words.

c. What is the probability that the proportion of people who will order coffee with

their meal is between 0.85 and 0.875?

d. What is the probability that the proportion of people who will order coffee with

their meal is at least 0.945?

28. Thirty percent of a magazine’s subscribers are female. A random sample of 50

subscribers is taken. Answer the following questions using Excel.

a. What is the probability that the proportion of females from this sample is at most

0.25?

b. What is the probability that the proportion of females from this sample is

between 0.22 and 0.28?

c. What is the probability that the proportion of females from this sample is within

.03 of the population proportion?

29. The proportion of Americans who support the death penalty is 0.53. A sample of 1000

randomly selected Americans is surveyed by telephone interview. Use Excel to answer

the following questions.

a. What is the probability that the sample proportion of those supporting the death

penalty will be less than 0.50?

b. What is the probability that the sample proportion of those supporting the death

penalty will be at least 0.55?

c. What is the probability that the sample proportion of those supporting the death

penalty will be between 0.50 and 0.55?

d. For samples of size 1000, 15% of all sample proportions are at most what value?

30. A random sample of nine telephone calls in an office provided the following information.

Call Number

Duration ( Minutes)

Type of Call

1

3

local

2

8

long distance

3

4

local

4

3

local

5

5

long distance

6

6

local

7

3

local

8

5

local

9

8

local

a. Determine the point estimate for the average duration of all calls.

b. What is the point estimate for the standard deviation of the population?

c. What is the point estimate for the proportion of all calls that were long distance?

31. A random sample of ten examination papers in a course that was given on a pass or fail

basis showed the following scores.

Paper Number

Grade

Status

1

65

Pass

2

87

Pass

3

92

Pass

4

35

Fail

5

79

Pass

6

100

Pass

7

48

Fail

8

74

Pass

9

79

Pass

10

91

Pass

a. What is the point estimate for the mean of the population?

b. What is the point estimate for the standard deviation of the population?

c. What is the point estimate for the proportion of all students who passed the

course?

32. Roger Hall, who oversees six Ford dealerships, believes that the colors chosen by

customers who special-order their cars best reflect most customers’ true color

preferences. For that reason, he has tabulated the color requests specified in a sample of

56 Mustang coupe special orders placed this year. The sample data are listed below.

Black

Red

White

Blue

Blue

Green

Red

Black

Red

White

Blue

White

Red

Red

Black

Black

Green

Black

Red

Black

Blue

Black

White

Green

Blue

Red

Black

White

Black

Red

Black

Blue

Blue

Black

Green

White

Black

Red

Red

White

Red

Red

Blue

Black

Red

Black

Green

Black

Green

Red

Black

White

Black

Red

Black

White

a. What is the point estimate of the proportion of all Mustang coupe special orders

that specify a color preference of black?

b. Describe the sampling distribution of

p

, where

p

is the proportion of Mustang

coupe special orders that specify a color preference of black. Assume that the

proportion of all Mustang coupe special orders having a color preference of black

is .36.

c. What is the probability that a simple random sample of 56 special orders will

provide an estimate of the population proportion of special orders specifying the

color black that is within plus or minus .05 of the actual population proportion,

assuming p = .36? In other words, what is the probability that

p

will be between

.31 and .41?

33. Missy Walters owns a mail-order business specializing in baby clothes. Missy is

confident the dollar amounts of all her orders are normally distributed or nearly so.

Assume she knows the mean and standard deviation are $249 and $46, respectively, for

all orders she receives.

a. Describe the sampling distribution of

x

, where

x

is the mean dollar-amount of

an order for a sample of 10 orders.

b. What is the probability that a simple random sample of 30 orders will provide an

estimate of the population mean dollar-amount of an order that is within plus or

minus $10 of the actual population mean?

c. What happens to the sampling distribution of

x

when the sample size is

increased from 30 to 90? With a sample size of 90, what is the probability that

x

will be between $239 and $259?

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