__
Business and Economics Statistics
__
11:373:215

**
Practice**__ Test Questions:__

__ __

__
Chapter 1
__

1. The incomes of a group of 50 loan applicants are obtained. Which level of measurement is incomes?

A) Nominal

B) Ordinal

C) Interval

D) Ratio

E) None of the above

2. What is a portion or part of a population called?

A) Random sample

B) Sample

C) Tally

D) Frequency distribution

E) None of the above

3. Which word is NOT part of the definition of descriptive statistics?

A) Organizing

B) Analyzing

C) Presenting

D) Predicting

E) None of the above

4. What type of data is the number of gallons of gasoline pumped by a filling station during a day?

A) Qualitative

B) Continuous

C) Attribute

D) Discrete

E) None of the above

5. The gathering, organizing, analyzing, and interpreting data is called

A) statistics.

B) descriptive statistics.

C) inferential statistics.

D) levels of measurement.

E) None of the above.

6. Which one of the following is NOT an example of discrete data?

A) Number of households watching the Home Improvement.

B) Number of employees reporting in sick.

C) Number of miles between New York City and Chicago.

D) Number of members of the Dobbs Ferry-Irvington Lions Club.

E) Number of family members.

7. The final rankings of the top 20 NCAA college basketball teams is an example
of which level of measurement?

A) Nominal

B) Ordinal

C) Interval

D) Ratio

E) None of the above

8. The names of the positions on a hockey team, such as forward and goalie, are
examples of what level of measurement?

A) Nominal

B) Ordinal

C) Interval

D) Ratio

E) None of the above

9. What type of data is the projected return on an investment?

A) Qualitative

B) Continuous

C) Attribute

D) Discrete

E) None of the above

**
Answer Key: Chapter 1
**
1. D

2. B

3. D

4. B

5. A

6. C

7. B

8. A

9. B

__
__

__
__

__
__

__
__

__
__

__
Chapter 2
__

1. What is the following table called?

Ages Number of Ages

20 up to 30 16

30 up to 40 25

40 up to 50 51

50 up to 60 80

60 up to 70 20

70 up to 80 8

A) Histogram

B) Frequency polygon

C) Ogive

D) Frequency distribution

E) None of the above

Use the following to answer questions 2-3:

Monthly commissions Class Frequencies

$ 600 up to $800 3

800 up to 1,000 7

1,000 up to 1,200 11

1,200 up to 1,400 22

1,400 up to 1,600 40

1,600 up to 1,800 24

1,800 up to 2,000 9

2,000 up to 2,200 4

2. What is the relative frequency for those salespersons who earn between $1,600 and $1,800?

A) 2%

B) 2.4%

C) 20%

D) 24%

E) None of the above

3. The first plot for a less-than cumulative frequency polygon be

A) X = 0, Y = 600.

B) X = 600, Y = 3.

C) X = 3, Y = 600.

D) X = 600, Y = 0.

E) none of the above.

Use the following to answer questions 4-6:

Refer to the following ages (rounded to the nearest whole year) of employees at
a large company that were grouped into a distribution with class limits: 20 up
to 30, 30 up to 40, 40 up to 50, 50 up to 60, and 60 up to 70.

4. The class limits for the class 50 up to 60 class are _______ and________ .

5. What is the midpoint for the class 40 up to 50? ________

6. What is the class interval? ______

Use the following to answer questions 7-9:

Hourly Wages Number of Wage Earners

$ 4 up to $7 18

7 up to 10 36

10 up to 13 20

13 up to 16 6

7. What is the class midpoint for the class with the greatest frequency?

A) $ 5.50

B) $ 8.50

C) $11.50

D) $14.50

E) None of the above

8. What is the class interval for the table of wages above?

A) $2

B) $3

C) $4

D) $5

E) None of the above

9. What are the class limits for the class with the smallest number of
frequencies?

A) 3.5 and 6.5

B) 4 and up to 7

C) 13 and up to 16

D) 12.5 and 15.5

E) None of the above

10. In a frequency distribution, what is the number of observations in a class
called?

A) Class midpoint

B) Class interval

C) Class array

D) Class frequency

E) None of the above

**
Answer Key: Chapter 2
**
1. A

2. C

3. D

4. 50 and up to 60

5. 45

6. 10 or ten

7. B

8. B

9. C

10. D

__Chapter 3
__

1. What are half of the observations always greater than?

A) Median

B) Mode

C) Mean

D) Geometric mean

E) None of the above

2. What must be the least scale of measurement for the median?

A) Nominal

B) Ordinal

C) Interval

D) Ratio

E) None of the above

3. Which measure of central tendency is used to determine the average annual percent increase?

A) Arithmetic mean

B) Weighted mean

C) Mode

D) Geometric mean

E) Median

4. Fifteen accounting majors had an average grade of 90 on a finance exam. Seven
marketing majors averaged 85, while ten finance majors averaged 93 on the same
exam. What is the weighted mean for the 32 students taking the exam?

A) 89.84

B) 89.33

C) 89.48

D) Impossible to determine without more information

E) None of the above

5. A sample of single persons receiving social security payments revealed these
monthly benefits: $826, $699, $1,087, $880, $839 and $965. How many observations
are below the median?

A) 0

B) 1

C) 2

D) 3

E) None of the above

6. The U.S. Federal Aviation Administration reported that passenger revenues on
international flights increased from $528 million in 1972 to $5,100 million in
1995. What is the geometric mean annual percent increase in international
passenger revenues?

A) 10.4

B) 27.9

C) 103.6

D) 9.96

E) None of the above

7. A sample of the paramedical fees charged by clinics revealed these amounts:
$55, $49, $50, $45, $52 and $55. What is the median charge?

A) $47.50

B) $51.00

C) $52.00

D) $55.00

E) None of the above

8. Which measure of central tendency is found by arranging the data from low to
high and selecting the middle value?

A) Arithmetic mean

B) Median

C) Mode

D) Geometric mean

E) None of the above

9. What is the median of 26, 30, 24, 32, 32, 31, 27 and 29?

A) 32

B) 29

C) 30

D) 29.5

E) None of the above

10. Based on the Empirical Rule, what percent of the observations will lie above
the mean plus two standard deviations?

A) 68%

B) 95%

C) 2.5%

D) 5%

**Answer Key: Chapter 3
**1. A

2. B

3. D

4. A

5. D

6. A

7. B

8. B

9. D

10. C

__
Chapter 4__

1. What do the quartile deviation and the interquartile range describe?

A) Lower 50% of the observations

B) Middle 50% of the observations

C) Upper 50% of the observations

D) Lower 25% and the upper 25% of the observations

E) None of the above

2. The coefficient of variation for a set of annual incomes is 18%; the
coefficient of variation for the length of service with the company is 29%. What
does this indicate?

A) More dispersion in the distribution of the incomes compared with the
dispersion of their length of service

B) More dispersion in the lengths of service compared with incomes

C) Dispersion in the two distributions (income and service) cannot be compared
using percents

D) Dispersions are equal

E) None of the above

3. What is the range for a sample of March electric bills amounts for
all-electric homes of similar sizes (to the nearest dollar): $212, $191, $176,
$129, $106, $92, $108, $109, $103, $121, $175 and $194.

A) $100

B) $130

C) $120

D) $112

E) None of the above

4. Which measure of dispersion disregards the algebraic signs (plus and minus)
of each difference between X and the mean?

A) Standard deviation

B) Mean deviation

C) Arithmetic mean

D) Variance

E) None of the above

5. What is the value of the coefficient of skewness for a distribution with a
mean of 17, median of 12 and standard deviation of 6?

A) +2.5

B) -2.5

C) +0.83

D) -0.83

E) None of the above

6. One-half the difference between the third and first quartiles is called?

A) Variance

B) Standard deviation

C) Quartile deviation

D) Interquartile range

E) None of the above

7. A study of business faculty at state supported institutions in Ohio revealed
that the arithmetic mean salary for nine months is $52,000 and a standard
deviation of $3,000. The study also showed that the faculty had been employed an
average (arithmetic mean) of 15 years with a standard deviation of 4 years. How
does the relative dispersion in the distribution of salaries compare with that
of the lengths of service?

A) Salaries about 100%, service about 50%

B) Salaries about 6%, service about 27%

C) Salaries about 42%, service about 81%

D) Salaries about 2%, service about 6%

E) None of the above

8. Where does the coefficient of variation generally lie between?

A) -1 and +1

B) -3 and +3

C) 0% and 100%

D) Unlimited values

E) None of the above

9. The weights of a sample of crates ready for shipment to Laos are (in
kilograms): 103, 97, 101, 106 and 103. What is the mean deviation?

A) 0 kg

B) 6.9 kg

C) 102.0 kg

D) 2.4 kg

E) None of the above

10. What is a disadvantage of the range as a measure of dispersion?

A) Based on only two observations

B) Can be distorted by a large mean

C) Not in the same units as the original data

D) Has no disadvantage

E) None of the above

**Answer Key: Chapter 4**

1. B

2. B

3. C

4. B

5. A

6. C

7. B

8. C

9. D

10. A

__
__

__
__

__
__

__
__

__
__

__
__

__
Chapter 5__

1. The National Center for Health Statistics reported that of every 883 deaths
in recent years, 24 resulted from an automobile accident, 182 from cancer and
333 from heart disease. Using the relative frequency approach, what is the
probability that a particular death is due to an automobile accident?

A) 24/883 or 0.027

B) 539/883 or 0.610

C) 24/333 or 0.072

D) 182/883 or 0.206

E) None of the above

2. A study of 200 stamping firms revealed these incomes after taxes:

Income After Taxes Number of Firms

Under $1 million 102

$1 million up to $20 million 61

$20 million and more 37

What is the probability that a particular firm selected has $1 millionor more in
income after taxes?

A) 0.00

B) 0.25

C) 0.49

D) 0.51

E) None of the above

3. Routine physical examinations are conducted annually as part of a health
service program for the employees. It was discovered that 8% of the employees
needed corrective shoes, 15% needed major dental work and 3% needed both
corrective shoes and major dental work. What is the probability that an employee
selected at random will need either corrective shoes or major dental work?

A) 0.20

B) 0.25

C) 0.50

D) 1.00

E) None of the above

4. A survey of top executives revealed that 35% of them regularly read Time
magazine, 20% read Newsweek and 40% read U.S. News & World Report. Ten percent
read both Time and U.S. News & World Report. What is the probability that a
particular top executive reads either Time or U.S. News & World Report
regularly?

A) 0.85

B) 0.06

C) 1.00

D) 0.65

E) None of the above

5. A tire manufacturer advertises that "the average life of our new all-season
radial tire is 50,000 miles. An immediate adjustment will be made on any tire
that does not last 50,000 miles." You purchased four of these tires. What is the
probability that all four tires will wear out before traveling 50,000 miles?

A) 1/10, or 0.10

B) ¼, or 0.25

C) 1/64, or 0.0156

D) 1/16, or 0.0625

E) None of the above

6. A sales representative calls on four hospitals in Westchester County. It is
immaterial what order he calls on them. How many ways can he organize his
calls?

A) 4

B) 24

C) 120

D) 37

E) None of the above

7. The machine has just been filled with 50 black, 150 white, 100 red and 100
yellow balls that have been thoroughly mixed. Sue and Jim approached the machine
first. They both said they wanted red gum balls. What is the likelihood they
will get their wish?

A) 0.50

B) 0.062

C) 0.33

D) 0.75

E) None of the above

8. There are two letters C and D. If repetitions such as CC are permitted, how
many permutations are possible?

A) 1

B) 0

C) 4

D) 8

E) None of the above

9. According to which classification or type of probability are the events
equally likely?

A) Classical

B) Relative frequency

C) Subjective

D) Mutually exclusive

E) None of the above

10. An experiment may have:

A) Only one result

B) Only two results

C) Two or more results

D) None of the above

11. Calculating the probability of an outcome is useful in the following except

A) inferential statistics.

B) descriptive statistics.

C) predicting a future outcome.

D) relative frequency.

E) none of the above.

**
Answer Key: Chapter 5
**
1. A

2. C

3. A

4. D

5. D

6. B

7. E

8. C

9. A

10. C

11. B

__
Chapter 6__

1. In which of the following discrete distribution does the probability of a
success vary from one trial to the next?

A) Binomial

B) Poisson

C) Hypergeometric

D) All of the above

E) None of the above

2. What is a listing of all possible outcomes of an experiment and their
corresponding probability of occurrence called?

A) Random variable

B) Probability distribution

C) Subjective probability

D) Frequency distribution

E) None of the above

3. Which of the following is correct about a probability distribution?

A) Sum of all possible outcomes must equal 1

B) Outcomes must be mutually exclusive

C) Probability of each outcome must be between 0 and 1 inclusive

D) All of the above

E) None of the above

4. The weight of an offensive linesman may be 210 pounds, 210.1 pounds, 210.13
pounds or 210.137 pounds depending on the accuracy of the scale. What is this an
illustration of?

A) Continuous random variable

B) Discrete random variable

C) Complement rule

D) All of the above

E) None of the above

5. Carlson Jewelers permits the return of their diamond wedding rings, provided
the return occurs within two weeks of the purchase date. Their records reveal
that 10 percent of the diamond wedding rings are returned. Five rings are bought
by five different customers. What is the probability that none will be
returned?

A) 0.250

B) 0.073

C) 0.590

D) 0.500

E) 0.372

6. Chances are 50-50 that a newborn baby will be a girl. For families with five
children, what is the probability that all the children are girls?

A) 0.100

B) 0.031

C) 0.001

D) 0.250

E) None of the above

7. What is the only variable in the Poisson probability formula?

A) m

B) x

C) e

D) P

E) None of the above

8. Which of the following is NOT a characteristic of a binomial probability
distribution?

A) Each outcome is mutually exclusive

B) Each trial is independent

C) Probability of success remains constant from trial to trial

D) Each outcome results from two trials

E) All of the above are characteristics of the binomial distribution

9. What must you know to develop a binomial probability distribution?

A) Probability of success

B) Number of trials

C) Number of successes

D) "a" and "b" only

E) "a" and "c" only

10. Sixty percent of the customers of a fast food chain order the Whopper,
french fries and a drink. If a random sample of 15 cash register receipts is
selected, what is the probability that 10 or more will show that the above three
food items were ordered?

A) 1,000

B) 0.186

C) 0.403

D) 0.000

E) None of the above

**
Answer Key: Chapter 6
**
1. C

2. B

3. D

4. A

5. C

6. B

7. B

8. D

9. D

10. C

__
Chapter 7__

1. Which of the following is NOT true regarding the normal distribution?

A) Mean, median and mode are all equal

B) It has a single peak

C) It is symmetrical

D) The points of the curve meet the X-axis at z = -3 and z = 3

E) None of the above

2. What is the area under the normal curve between z = -1.0 and z = -2.0?

A) 0.0228

B) 0.3413

C) 0.1359

D) 0.4772

E) None of the above

3. For the normal distribution, the mean plus and minus 1.96 standard deviations
will include about what percent of the observations?

A) 50%

B) 99.7%

C) 95%

D) 68%

E) None of the above

4. For a standard normal distribution, what is the probability that z is greater
than 1.75?

A) 0.0401

B) 0.0459

C) 0.4599

D) 0.9599

E) None of the above

5. What is the area under the normal curve for z = 1.79?

A) 0.4633

B) 0.0367

C) 0.9599

D) 0.0401

E) None of the above

6. The mean amount spent by a family of four on food per month is $500 with a
standard deviation of $75. Assuming that the food costs are normally
distributed, what is the probability that a family spends less than $410 per
month?

A) 0.2158

B) 0.8750

C) 0.0362

D) 0.1151

E) None of the above

7. Which of the following is NOT a characteristic of the normal probability
distribution?

A) Positively-skewed

B) Bell-shaped

C) Symmetrical

D) Asymptotic

E) All of the above

8. The mean of a normally distributed group of weekly incomes of a large group
of executives is $1,000 and the standard deviation is $100. What is the z-score
for an income of $1,100?

A) 1.00

B) 2.00

C) 1.683

D) -0.90

E) None of the above

9. The mean of a normal distribution is 400 pounds. The standard deviation is 10
pounds. What is the area between 415 pounds and the mean of 400 pounds?

A) 0.5000

B) 0.1932

C) 0.4332

D) 0.3413

E) None of the above

10. Which of the following is true in a normal distribution?

A) Mean equals the mode and the median

B) Mode equals the median

C) Mean divides the distribution into two equal parts

D) All of the above are correct

E) None of the above

11. What is the distribution with a mean of 0 and a standard deviation of 1
called?

A) Frequency distribution

B) z-score

C) Standard normal distribution

D) Binomial probability distribution

E) None of the above

12. The annual commissions per salesperson employed by a manufacturer of light
machinery averaged $40,000 with a standard deviation of $5,000. What percent of
the sales persons earn between $32,000 and $42,000?

A) 60.06%

B) 39.94%

C) 34.13%

D) 81.66%

E) None of the above

**Answer Key: Chapter 7
**1. D

2. C

3. C

4. A

5. B

6. D

7. A

8. A

9. C

10. D

11. C

12. A

__
Chapter 8__

1.What is it called when all the items in the population have the same chance of
being selected for the sample?

A)Nonprobability sampling

B)Random sampling

C)Judgement sampling

D)Cluster sampling

E)None of the above

2.What sample statistic is used to estimate a population value?

A)Parameter

B)Sampling error

C)Point estimate

D)Interval estimate

E)None of the above

3.Suppose we select every fifth invoice in a file.What type of sampling is this?

A)Random

B)Cluster

C)Stratified

D)Systematic

E)None of the above

4.If the level of confidence is lowered from 95% to 90%, but the allowable error
and the standard deviation remain the same, what happens to the required sample
size?

A)Increases

B)Decreases

C)Remains unchanged

D)None of the above

5.In a sample of 2,000 persons, 1,600 favored more strict environmental
protection measures.What is the estimated population proportion?

A)0.16 or 16%

B)0.20 or 20%

C)0.80 or 80%

D)0.82 or 82%

E)None of the above

6.A random sample of 85 group leaders, supervisors, and similar personnel
revealed that on the average a person spent 6.5 years on the job before being
promoted.The standard deviation of the sample was 1.7 years.Using the 0.95
degree of confidence, what is the confidence interval within which the
population mean lies?

A)6.99 and 7.99

B)4.15 and 7.15

C)6.14 and 6.86

D)6.49 and 7.49

E)None of the above

7.A statewide sample survey is to be made.First, the state is subdivided into
counties.Seven counties are selected at random and further sampling is
concentrated on these seven counties.What type of sampling is this?

A)Simple random

B)Nonproportional

C)Cluster

D)Stratified

E)None of the above

8.Which of the following is NOT a valid reason for selecting a sample instead of
studying the whole population?

A)Cost of studying an entire population can be too high

B)Population can be destroyed in the process of studying it

C)Study of the population can be too time consuming

D)Sample results have a more accuracy than population results

E)All of the above reasons are valid

9.For a population that is not normally distributed, the distribution of the
sample means will

A)be negatively skewed.

B)approach the normal distribution.

C)be positively skewed.

D)take the same shape as the population.

E)none of the above.

10.Which of the following is NOT necessary to determine how large a sample to
select from a population?

A)Level of confidence in estimating the population parameter

B)Size of the population

C)Maximum allowable error in estimating the population parameter

D)Estimate of the population variation

E)All of the above are necessary

**Answer Key: Ch. 8**

1.B

2.C

3.D

4.B

5.C

6.C

7.C

8.D

9.B

10.B

__Chapter 9 __

1. What is the level of significance?

A) Probability of a Type II error

B) Probability of a Type I error

C) z-value of 1.96

D) Beta error

E) None of the above

2. What do we call the conditions under which the null hypothesis is NOT
rejected?

A) Decision rule

B) Test statistic

C) Alternate hypothesis

D) Critical value

E) None of the above

3. If the alternate hypothesis states that m does not equal 4,000, what is the
rejection region for the hypothesis test?

A) Both tails

B) Lower or left tail

C) Upper or right tail

D) Center

E) None of the above

4. If the 1% level of significance is used and the computed value of z is +6.00,
what is our decision?

A) Do not reject H0

B) Reject H0

C) Reject H1

D) None of the above

5. What is another name for the alternate hypothesis?

A) Null hypothesis

B) Hypothesis of no difference

C) Rejected hypothesis

D) Research hypothesis

E) None of the above

6. What is the critical z-value for a one-tailed lower test at the 1% level of
risk?

A) + 2.58

B) - 2.58

C) + 2.33

D) - 2.33

E) None of the above

7. Which of the following is a test statistic used to test a hypothesis about a
population?

A) a

B) b

C) m

D) z

E) None of the above

8. If the alternative hypothesis states that m > 6,700, what is the rejection
region for the hypothesis test?

A) Both tails

B) Lower tail

C) Upper tail

D) Center

E) None of the above

9. If the critical value for a test statistic equals 2.45, what value of the
test statistic would guarantee no chance of making a Type I error?

A) 3.74

B) 2.14

C) 2.46

D) 4.56

E) None of the above

10. Suppose we are testing the difference between two proportions at the 0.05
level of significance. If the computed z is -1.07, what is our decision?

A) Reject the null hypothesis

B) Do not reject the null hypothesis

C) Take a larger sample

D) Reserve judgment

E) None of the above

11. If two proportions are being studied, what is the value of pc computed from
the combined sample information?

A) Always equal p1

B) Always equal p1

C) Always be between X1 and X2

D) None of the above

12. If 20 out of 50 students sampled live in a college dormitory, what is the
estimated proportion of students at the University living in a dormitory?

A) 0.20

B) 0.40

C) 0.50

D) 0.60

E) None of the above

13. What is the sample proportion defined as?

A) np

B) x/n

C) n!

D) p

E) None of the above

**Answer Key: Ch. 9**

1. B

2. A

3. A

4. B

5. D

6. D

7. D

8. C

9. B

10. B

11. C

12. B

13. B

__Chapter 10__

1.The mean length of a small counter balance bar is 43 millimeters. There is
concern that the adjustments of the machine producing the bars have changed.
Test the claim at the 0.02 level that there has been no change in the mean
length. The alternate hypothesis is that there has been a change. Twelve bars(n=
12) were selected at random and their lengths recorded. The lengths are (in
millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43 and 42.The mean of the
sample is 41.5 and the standard deviation 1.784.Computed t = - 2.913.Has there
been a statistically significant change in the mean length of the bars?

A)Yes, because the computed t lies in the area beyond the critical.

B)No, because the information given is not complete.

C)No, because the computed t lies in the area to the right of -2.913.

D)None of the above

2.The net weights of a sample of bottles filled by a machine manufactured by
Edne, and the net weights of a sample filled by a similar machine manufactured
by Orno, Inc., are (in grams):

Edne:5, 8, 7, 6, 9 and 7

Orno:8, 10, 7, 11, 9, 12, 14 and 9

Testing the claim at the 0.05 level the mean weight of the bottles filled by the
Orno machine is greater than the mean weight of the bottles filled by the Edne
machine, what is the critical value?

A)-1.96

B)-2.837

C)-6.271

D)+3.674

E)None of the above

3.Which of the following conditions must be met to conduct a test for the
difference in two sample means?

A)Data must be of interval scale

B)Populations must be normal

C)Variances in the two populations must be equal

D)All the above are correct

E)None of the above are correct

4.Which statement(s) is/are correct about the t distribution?

A)Mean = 0

B)Symmetric

C)Based on degrees of freedom

D)All of the above are correct

E)None of the above are correct

5.A random sample of size 15 is selected from a normal population. The
population standard deviation is unknown.Assume that a two-tailed test at the
0.10 significance level is to be used.For what value of t will the null
hypothesis not be rejected?

A)To the left of-1.282 or to the right of 1.282

B)To the left of -1.345 or to the right of 1.345

C)To the left of -1.761 or to the right of 1.761

D)To the left of -1.645 or to the right of 1.645

E)None of the above

6.To conduct a test of hypothesis with a small sample, we need to be able to
make the following assumption that:

A)a larger computed value oftwill be needed to reject the null hypothesis

B)the region of acceptance will be wider than for large samples

C)the confidence interval will be wider than for large samples

D)the population is normally distributed.

E)None of the above

7.How does thetdistribution differ from the standard z distribution?

A)Continuous distribution

B)Bell-shaped

C)Family of distributions

D)Symmetrical

E)None of the above

8.What is the critical value for a one-tailed hypothesis test in which a null
hypothesis is tested at the 5% level of significance based on a sample size of
25?

A)1.708

B)1.711

C)2.060

D)2.064

E)None of the above

9.A sample of 20 is selected from the population.What is the number of degrees
of freedom used to determine the appropriate criticalt-value?

A)20

B)19

C)21

D)25

E)None of the above

10.If two samples are used in a hypothesis test for which the combined degrees
of freedom is 24, which one of the following is NOT true about the two sample
sizes?

A)Sample A = 11; sample B = 13

B)Sample A = 12; sample B = 14

C)Sample A = 13; sample B = 13

D)Sample A = 10; sample B =16

E)Cannot determine from the above information

11.The t distribution is similar to the z distribution in all BUT one of the
following characteristics.Which one is it?

A)Continuous

B)Symmetrical

C)Bell-shaped

D)Only one for a given mean

E)None of the above

**Answer Key: Ch. 10**

1.A

2.E

3.D

4.D

5.C

6.D

7.C

8.B

9.B

10.A

11.D

__
Chapter11__

1. The term "ANOVA"

A. Has no special meaning.

B. Stands for Analysis of Variance.

C. Stands for Another Numerical Observation of the Variance.

D. None of the above.

2. The general idea of analysis of variance is to compare estimates of variance

A. From both between and within the means

B. Based on the several treatments.

C. From within the treatments.

D. None of the above.

3. Which of the following is not a characteristic of the F distribution?

A. It is a discrete distribution.

B. In cannot be negative.

C. It is based on two sets of degrees of freedom.

D. All of the above.

4. The term "treatment" refers to

A. Source of variation.

B. The numerator degrees of freedom.

C. The variation within the cells.

D. None of the above.

5. Suppose we select 6 observations from each of three treatments. The
appropriate degrees of freedom are

A. 3 and 6.

B. 2 and 6.

C. 2 and 15.

D. None of the above

6. The term MSE

A. Is called the sum of squares error.

B. Is found by SSE/(n - k ).

C. Is an estimate of the common population variance.

D. All of the above.

7. Which of the following is not an assumption required for ANOVA?

A. The populations are normally distributed.

B. The populations have equal standard deviations.

C. The samples are independent.

D. All of the above are assumptions required for ANOVA.

8. In a two-way ANOVA the second source of variation is due to

A. Random error.

B. Blocks.

C. Total variation.

D. None of the above

9. Under which of the following conditions will the computed value of F be
negative?

A. When there is no difference in the treatment means

B. When there is no difference in the block means

C. When the SS total is larger than SST.

D. F cannot be negative.

10. Suppose we conduct an ANOVA test of four treatment means and reject the null
hypothesis. Construction of a confidence interval for the difference between the
first and second sample mean revealed the interval to be 10 plus or minus 12. We
conclude

A. This pair of means differ.

B. This pair of means does not differ.

C. Because we do not know the units involved, we cannot draw any conclusion.

D. Because we do not know the degrees of freedom, we can not draw any
conclusion.

11. A package delivery company purchased five trucks from manufacturer A, four
from B, and five from C. They then recorded and compared the maintenance cost of
each truck. To apply the F test, how many degrees of freedom are in the
denominator?

A. 2

B. 3

C. 11

D. 14

12. In an effort to teach quality principles to a group, four different methods
were used. Scores on a standard test for five employees in each of the four
groups were then obtained. What is the critical value for a test at the 0.01
significance level?

A. 1.00

B. 1.96

C. 3.24

D. 5.29

**
Answer Key: Ch. 11
**
1.B

2.A

3.A

4.D

5.C

6.B

7.D

8.B

9.D

10.B

11.C

12.D

__
Chapter 12__

1. A scatter diagram is a chart

A. In which the dependent variable is scaled along the vertical axis.

B. In which the independent variable is scaled along the horizontal axis.

C. That portrays the relationship between two variables.

D. All of the above.

2. In correlation analysis

A. We consider several independent variables.

B. We study the strength of the association between two variables.

C. We report the percent of the explained variation.

D. None of the above.

3. The sample coefficient of correlation

A. Has the same sign as the slope, i.e. b.

B. Can range from -1.00 up to 1.00

C. Is also called Pearson's r .

D. All of the above.

4. The coefficient of determination

A. Is the square of the coefficient of correlation.

B. Cannot be negative.

C. Reports the percent of the variation in the dependent variable explained by
the independent variable.

D. All of the above.

5. Suppose we developed the following least squares regression equation: Y¢ =
3.5 + 2.1X. Which of the following statement is correct?

A. The dependent variable increases 2.1 for an increase of 1 in X.

B. The equation crosses the Y axis at 3.5.

C. If X = 5, then Y¢ = 14.

D. All of the above.

6. The standard error of estimate is

A. Based on squared deviations from the regression line.

B. May assume negative values.

C. Is in squared units of the dependent variable.

D. All of the above.

7. Which of the following is not a necessary condition for regression analysis.

A. The standard deviation of each of the conditional distributions must be the
same.

B. The Y values are independent.

C. For each X value, there is a group of Y values and these Y values are
normally distributed.

D. The slope of the regression line is positive (increasing).

8. Which of the following is not based on squared deviations from the regression
line?

A. The coefficient of correlation.

B. The coefficient of determination.

C. The standard deviation.

D. The standard error of estimate.

9. In an ANOVA table for regression, the degrees of freedom for regression is

A. Always equal to 1.

B. n - 1.

C. n - 2.

D. None of the above.

10. The term SSR/SS total is also called the

A. Sum of squares due to regression.

B. Coefficient of determination.

C. Standard error of estimate.

D. Coefficient of correlation.

11. If r = 0.89, what is the coefficient of determination?

A. 0.94

B. 0.89

C. 0.79

D. 0.06

12. A hypothesis test is conducted at the .05 level of significance to test
whether the population correlation is zero. If the sample consists of 25
observations and the correlation coefficient is 0.60, then what is the computed
value of the test statistic?

A. 1.96

B. 2.07

C. 2.94

D. 3.60

**
Answer Key: Ch. 12
**
1.D

2.B

3.D

4.D

5.D

6.A

7.D

8.C

9.D

10.B

11.C

12.D

__
Chapter 13__

1.Which test statistic do we apply to test the null hypothesis that the multiple
regression coefficients are all zero?

A)z

B)t

C)F

D)SPSS-X

E)None of the above

2.What is the range of values for multiple R?

A)-1.00 to -1.00 inclusive

B)-1.00 to 0 inclusive

C)0 to +1.00 inclusive

D)Unlimited range

E)None of the above

3.What is it called when the independent variables are highly correlated?

A)Autocorrelation

B)Multicollinearity

C)Homoscedasticity

D)Zero correlation

E)None of the above

4.What test investigates whether all the independent variables have zero net
regression coefficients?

A)Multicollinearity

B)Autocorrelation

C)Global

D)Pearson

E)None of the above

5.If there are four independent variables in a multiple regression equation,
there are also four

A)Y-intercepts.

B)regression coefficients.

C)dependent variables.

D)constant terms.

E)None of the above.

6.How is the Y intercept in the multiple regression equation represented?

A)b1

B)x1

C)b2

D)x2

E)None of the above

7.What is the degrees of freedom associated with the regression sum of squares?

A)Number of independent variables

B)1

C)F-ratio

D)(n - 2)

E)None of the above

8.The coefficient of determination measures the proportion of

A)explained variation.

B)variation due to the relationship among variables.

C)error variation.

D)variation due to regression.

E)none of the above.

9.What happens as the scatter of data values about the regression plane
increases?

A)Standard error of estimate increases

B)R2 decreases

C)(1 - R2) increases

D)Residual sum of squares increases

E)All of the above are correct

10.Multiple regression is an analytical procedure involving the possible
relationship of?

A)An independent variable to several dependent variables

B)A dependent variable to several independent variables

C)Several dependent variables to several independent variables

D)Several regression equations to a single sample

E)None of the above

**Answer Key: Ch. 13
**1.C

2.C

3.B

4.C

5.B

6.E

7.A

8.A

9.E

10.B

__
Chapter14__

1. What is the critical value at the 0.05 level of significance for a
goodness-of-fit test if there are six categories?

A) 3.841

B) 5.991

C) 7.815

D) 11.070

E) None of the above

2. The chi-square distribution can assume

A) only positive values.

B) only negative values.

C) negative and positive values or zero.

D) only zero.

E) none of the above.

3. What is our decision for a goodness-of-fit test with a computed value of
chi-square of 1.273 and a critical value of 13.388?

A) Do not reject the null hypothesis

B) Reject the null hypothesis

C) Unable to reject or not reject the null hypothesis based on data

D) Should take a larger sample

E) None of the above

4. Which of the following are correct statements regarding the chi-square
distribution?

A) Distribution is negatively skewed

B) Chi-square is based on two sets of degrees of freedom, one for the numerator
and one for the denominator

C) Its shape is based on the degrees of freedom

D) All of the above are true

E) None of the above are true

5. Which of the following are correct statements regarding the goodness-of-fit
test?

A) Data may be of nominal scale

B) Population must be normal

C) All the expected frequencies must be equal

D) All of the above are true

E) None of the above are true

6. For any chi-square goodness-of-fit problem, the number of degrees of freedom
is found by

A) n - k - 1.

B) k - 1.

C) n + 1.

D) n + k.

E) none of the above.

7. The test whether two variables or characteristics are related results in

A) a contingency table.

B) a chi-square table.

C) an ANOVA table.

D) a scatter diagram.

E) none of the above.

8. When determining how well an observed set of frequencies fit an expected set
of frequencies the test is the

A) F test.

B) t test.

C) goodness-of-fit test

D) test for association.

E) none of the above.

9. In the chi-square test, the null hypothesis (no difference between sets of
observed and expected frequencies) is rejected when the

A) computed chi-square is less then the critical value.

B) difference between the observed and expected frequencies is significant.

C) difference between the observed and expected frequencies is small.

D) difference between the observed and expected frequencies occurs by chance.

E) none of the above.

10. The computed value of chi-square is always positive because the difference
between the observed frequencies and the expected frequencies are?
________________

**Answer Key: Ch. 14**

1. D

2. A

3. A

4. C

5. A

6. B

7. A

8. C

9. B

10. squared