Test bank for statistics for the behavioral sciences 9th edition by gravetter download

Test Bank for Statistics for the Behavioral Sciences 9th
Edition by Gravetter
Chapter 1: Introduction to Statistics
Chapter Outline
1.1 Statistics, Science, and Observation
Definitions of Statistics
1.2 Populations and Samples
What are They?
Variables and Data
Parameters and Statistics
Descriptive and Inferential Statistical Methods
Statistics in the Context of Research
1.3 Data Structures, Research Methods, and Statistics
Individual Variables
Relationships between Variables
The Experimental Method
Nonexperimental Methods: Nonequivalent Groups and Pre-Post Studies
Data Structures and Statistical Methods
1.4 Variables and Measurement
Constructs and Operational Definitions
Discrete and Continuous Variables
Scales of Measurement
The Nominal Scale
The Ordinal Scale
The Interval and Ratio Scales
Statistics and Scales of Measurement
1.5 Statistical Notation
Summation Notation

Learning Objectives and Chapter Summary
Instructor Notes - Chapter 1 - page 1

1. Students should be familiar with the terminology and special notation of statistical
analysis. The terminology consists of:
Statistical Terms
population
sample
parameter
statistic
descriptive statistics
inferential statistics
sampling error

Measurement Terms
operational definition
nominal
ordinal
interval
ratio
discrete variable
continuous variable
real limits

Research Terms
correlational method
experimental method
independent variable
dependent variable
nonexperimental method
quasi-independent variable

Figure 1.1 is useful for introducing the concepts of population and sample, and the related
concepts of parameter and statistic. The same figure also helps differentiate descriptive
statistics that focus on the sample data and inferential statistics that are used to generalize
from samples to populations.

2. Students should learn how statistical techniques fit into the general process of science.
Although the concept of sampling error is not critical at this time in the course, it is a
useful way to introduce and justify the need for inferential statistics. Figure 1.2 is a
simple demonstration of the concept that sample statistics are representative but not
identical to the corresponding population parameters, and that two different samples will
tend to have different statistics. The idea that differences can occur just by chance is the
important concept. After the concept of sampling error is established, Figure 1.3 shows
the overall research process and identifies where descriptive statistics are used and
where inferential statistics are used.
Statistical techniques are used near the end of the research process, after the researcher
has obtained research results and needs to organize, summarize and interpret the data.
Chapter 1 includes discussion of two aspects of research that precede statistics: (1) the
process of measurement, and (2) the idea that measurements take place in the context of a
research study. The discussion includes the different scales of measurement and the
information they provide, as well as an introduction to continuous and discrete variables.
Research studies are described in terms of the kinds of data they produce: correlational
studies that produce data suitable for computing correlations (see Figure 1.4), and
experimental studies that produce groups of scores to be compared, usually looking for
mean differences (see Figure 1.6). Other types of research (non-experimental) that also
involve comparing groups of scores are also discussed (see Figure 1.7).

Instructor Notes - Chapter 1 - page 2

3. Students should learn the notation, particularly the summation notation, that will be used
throughout the rest of the book.
There are three key concepts important to using summation notation:
1. Summation is a mathematical operation, just like addition or multiplication, and the
different mathematical operations must be performed in the correct order (see Order of
Mathematical Operations, page 25).
2. In statistics, mathematical operations usually apply to a set of scores that can
be presented as a column of numbers.
3. Each operation, except for summation, creates a new column of numbers. Summation,
calculates the sum for the column.

Other Lecture Suggestions
1. Early in the first class I acknowledge that
a. Most students are not there by choice. (No one picked Statistics as an elective because
it looked like a fun class.)
b. Many students have some anxiety about the course.
However, I also try to reassure them that the class will probably be easier and more
enjoyable (less painful) than they would predict, provided they follow a few simple rules:
a. Keep Up. In statistics, each bit of new material builds on the previous material. As
long as you have mastered the old material, then the new stuff is just one small step
forward. On the other hand, if you do not know the old material, then the new stuff is
totally incomprehensible. (For example, try reading Chapter 10 on the first day of
class. It will make no sense at all. However, by the time we get to Chapter 10, you
will have enough background to understand it.) Keeping up means coming to class,
asking questions, and doing homework on a regular basis. If you are getting lost, then
get help immediately.
b. Test Yourself. It is very easy to sit in class and watch an instructor work through
examples. Also, it is very easy to complete homework assignments if you can look
back at example problems in the book. Neither activity means that you really know
the material. For each chapter, try one or two of the end-of-chapter problems without

looking back at the examples in the book or checking your notes. Can you really do
the problems on your own? If not, pay attention to where you get stuck in the
problem, so you will know exactly what you still need to learn.
2. Give students a list of variables, for example items from a survey (age, gender, education
level, income, occupation) and ask students to identify the scale of measurement most likely
to be used and whether the variable is discrete or continuous.

Instructor Notes - Chapter 1 - page 3


3. Describe a non-experimental or correlational study and have students identify reasons that
you cannot make a cause-and-effect conclusion from the results. For example, a researcher finds
that children in the local school who regularly eat a nutritious breakfast have higher grades than
students who do not eat a nutritious breakfast. Does this mean that a nutritious breakfast causes
higher grades. For example, a researcher finds that employees who regularly use the company’s
new fitness center have fewer sick days than employees who do not use the center. Does this
mean that using the fitness center causes people to be healthier?
In either case, describe how the study could be made into an experiment by
a. beginning with equivalent groups (random assignment).
b. manipulating the independent variable (this introduces the ethical question of forcing
people to eat a nutritious breakfast).
c. controlling other variables (the rest of the children’s diet).
4 After introducing some basic applications of summation notation, present a simple list of
scores (1, 3, 5, 4) and a relatively complex expression containing summation notation, for
2
example, Σ(X – 1) . Ask the students to compute the answer. You are likely to obtain several
different responses.
Note that this is not a democratic process - the most popular answer is not necessarily
correct. There is only one correct answer because there is only one correct sequence for
performing the calculations. Have the class identify the step by step sequence of operations

specified by the expression. (First, subtract 1 from each of the scores. Second, square the
resulting values. Third, sum the squared numbers.) Then apply the steps, one by one, to
compute the answer. As a variation, present a list of steps and ask students to write the
mathematical expression corresponding to the series of steps.

Instructor Notes - Chapter 1 - page 4


Exam Items for Chapter 1
Multiple-Choice Questions
Note: Questions identified with (www) are available to students as a practice quiz on the
cengage.com/psychology/gravetter website.

1. A researcher uses an anonymous survey to investigate the study habits of American college
students. The entire group of American college students is an example of a(n) _________.
a. sample
b. statistic
c. population
d. parameter
2. A researcher uses an anonymous survey to investigate the study habits of American college
students. Based on the set of 56 surveys that were completed and returned, the researcher finds
that these students spend an average of 4.1 hours each week working on course material outside
of class. For this study, the set of 56 students who returned surveys is an example of a(n)
_______.
a. parameter
b. statistic
c. population
d. sample
3. (www) A researcher uses an anonymous survey to investigate the study habits of American
college students. Based on the set of 56 surveys that were completed and returned, the researcher

finds that these students spend an average of 4.1 hours each week working on course material
outside of class. For this study, the average of 4.1 hours is an example of a(n) _______.
a. parameter
b. statistic
c. population
d. sample

4. A researcher is interested in the eating behavior of rats and selects a group of 25 rats to be
tested in a research study. The group of 25 rats is an example of a ______.
a. sample
b. statistic
c. population
d. parameter

Instructor Notes - Chapter 1 - page 5


5. A researcher is curious about the average monthly cell phone bill for high school students in
the state of Florida. If this average could be obtained, it would be an example of a ______.
a. sample
b. statistic
c. population
d. parameter
6. (www) Although a research study is typically conducted with a relatively small group of
participants known as a _________, most researchers hope to generalize their results to a much
larger group known as a _________.
a. sample, population
b. statistic, sample
c. population, sample
d. parameter, population

7. The relationship between a statistic and a parameter is the same as the relationship between
______.
a. a sample and a population.
b. a statistic and a parameter.
c. a parameter and a population
d. descriptive statistics and inferential statistics.
8. (www) Statistical methods that organize, summarize, or simplify data are called _______.
a. parameters
b. statistics
c. descriptive statistics
d. inferential statistics
9. A characteristic, usually a numerical value, that describes a sample is called a _______.
a. parameter
b. statistic
c. variable
d. constant
10. A researcher records the change in weight (gain or lost) during the first semester of college
for each individual in a group of 25 freshmen, and calculates the average change in weight. The
average is an example of a _______.
a. parameter
b. statistic
c. variable
d. constant

Instructor Notes - Chapter 1 - page 6


11. The average verbal SAT score for the entire class of entering freshmen is 530. However, if
you select a sample of 20 freshmen and compute their average verbal SAT score you probably
will not get exactly 530. What statistical concept is used to explain the natural difference that

exists between a sample mean and the corresponding population mean?
a. statistical error
b. inferential error
c. sampling error
d. parametric error
12. A researcher conducts an experiment to determine whether moderate doses of St. Johns
Wort have any effect of memory for college students. For this study, what is the independent
variable?
a. the amount of St. Johns Wort given to each participant
b. the memory score for each participant
c. the group of college students
d. cannot answer without more information
13. (www) A recent study reports that elementary school students who were given a
nutritious breakfast each morning had higher test scores than students who did not receive the
breakfast. For this study, what is the independent variable?
a. the students who were given the nutritious breakfast
b. the students who were not given the nutritious breakfast
c. whether or not a breakfast was given to the students
d. the test scores for the students
14. In a correlational study
a. 1 variable is measured and 2 groups are compared
b. 2 variables are measured and 2 groups are compared
c. 1 variable is measured and there is only 1 group of participants
d. 2 variables are measured and there is only 1 group of participants
15. In an experimental study
a. 1 variable is measured and 2 groups are compared
b. 2 variables are measured and 2 groups are compared
c. 1 variable is measured and there is only 1 group of participants
d. 2 variables are measured and there is only 1 group of participants
16. For a research study comparing attitude scores for males and females, participant gender is

an example of what kind of variable?
a. an independent variable
b. a dependent variable
c. a quasi-independent variable
d. a quasi-dependent variable

Instructor Notes - Chapter 1 - page 7


17. For an experiment comparing two methods for teaching social skill training to autistic
children, the independent variable is _______ and the dependent variable is _______.
a. teaching methods, the autistic children
b. the autistic children, the social skills that are learned
c. the social skills that are learned, the autistic children
d. teaching methods, the social skills that are learned
18. Which of the following is an example of a discrete variable?
a. the age of each student in a psychology class
b. the gender of each student in a psychology class
c. the amount of time to solve a problem
d. the amount of weight gained for each freshman at a local college

19. (www) Which of the following is an example of a continuous variable?
a. the gender of each student in a psychology class
b. the number of males in each class offered by the college
c. the amount of time to solve a problem
d. number of children in a family
20. If it is impossible to divide the existing categories of a variable, then it is an example of a
_____ variable.
a. independent
b. dependent

c. discrete
d. continuous
21. (www) Using letter grades (A, B, C, D, and E) to classify student performance on an exam
is an example of measurement on a(n) _______ scale of measurement.
a. nominal
b. ordinal
c. interval
d. ratio
st

nd

22. Determining the class standing (1 , 2 , and so on) for the graduating seniors at a
high school would involve measurement on a(n) _____ scale of measurement.
a. nominal
b. ordinal
c. interval
d. ratio

Instructor Notes - Chapter 1 - page 8


23. (www) What additional information is obtained by measuring two individuals on an
interval scale compared to a ordinal scale?
a. whether the measurements are the same or different
b. the direction of the difference
c. the size of the difference
d. none of the other options is correct
24. Determining a person's reaction time (in milliseconds) would involve measurement on a(n)
_____ scale of measurement.

a. nominal
b. ordinal
c. interval
d. ratio

25. After measuring two individuals, a researcher can say that Tom’s score is 4 points higher
than Bill’s. The measurements must come from a(n) _______ scale.
a. nominal
b. ordinal
c. interval
d. interval or ratio
26. (www) What is the first step to be performed in the following mathematical expression?
2
(ΣX)
a. Square each score.
b. Add the scores.
c. Add the squared scores.
d. Square the sum of the scores.
2

27. What is the final step to be performed in the following mathematical expression? (ΣX) ?
a. Square each score.
b. Add the scores.
c. Add the squared scores.
d. Square the sum of the scores.
2

28. What is the final step to be performed when computing Σ(X – 2) ?
a. square each value
b. subtract 2 points from each score

c. sum the squared values
2
2
d. subtract 2 from each X value

Instructor Notes - Chapter 1 - page 9


2

29. What is the value of (ΣX) for the following scores? Scores: 1, 5, 2
a. 10
b. 16
c. 30
d. 64
2

30. What is the value of ΣX for the following scores?
a. 14
b. 21
Scores: 1, 0, 2, 4
c. 28
d. 49
31. What is the value of ΣX + 1 for the following scores?
a. 8
b. 10
Scores: 1, 0, 2, 4
c. 11
d. 14
32. (www) What is the value of Σ(X + 1) for the following scores?

a. 4
b. 6
Scores: 1, 0, 1, 4
c. 7
d. 10
2

33. What is the value of Σ(X – 1) for the following scores?
a. 10
b. 16
Scores: 1, 2, 1, 4
c. 36
d. 49
2

34. What is the value of (ΣX) for the following scores?
a. 14
b. 21
Scores: 1, 0, 2, 4
c. 28
d. 49
35. What is the value of ΣX + 1 for the following scores? Scores: 1, 6, 3
a. 10
b. 11
c. 13
d. 16

Instructor Notes - Chapter 1 - page 10

36. What is the value of Σ(X + 1) for the following scores? Scores: 2, 4, 7.
a. 10
b. 11
c. 13
d. 16
37. What is the value of Σ(X – 2) for the following scores? Scores: 2, 3, 5
a. 4
b. 6
c. 8
d. 10
2

38. (www) What is the value of Σ(X – 2 ) for the following scores? Scores: 2, 3, 5
a. 8
b. 10
c. 16
d. 36
39. You are instructed to subtract four points from each score and find the sum of the resulting
values. How would this set of instructions be expressed in summation notation?
a. ΣX – 4
b. Σ (X – 4)
c. 4 – ΣX
d. Σ(4 – X)
40. You are instructed to subtract four points from each score, square the resulting value,
and find the sum of the squared numbers. How would this set of instructions be expressed in
summation notation?
2
a. ΣX – 4
2
b. (ΣX – 4)

c.

Σ(X – 4)

2

2

d. ΣX – 4
True/False Questions

41. Using the average score to describe a sample is an example of inferential statistics.
42. A researcher is interested in the average income for registered voters in the United
States. The entire group of registered voters is an example of a population.
43. The average score for a population is an example of a statistic.

Instructor Notes - Chapter 1 - page 11


44. A researcher interested in vocabulary development obtains a sample of 3-year-old
children to participate in a research study. The average score for the group of 20 is an example
of a parameter.
45. The goal for an experiment is to demonstrate that changes in one variable are responsible for
causing changes in a second variable.
46. An experimental research study typically involves measuring two scores for each
individual in one group of participants.
47. A correlational study typically uses only one group of participants but measures
two different variables (two scores) for each individual.
48. A correlational study is used to examine the relationship between two variables but
cannot determine whether it is a cause-and-effect relationship.

49. A recent report concluded that children with siblings have better social skills than
children who grow up as an only child. This is an example of an experimental study.
50. A recent report concluded that college graduates have higher life-satisfaction scores than
individuals who do not receive college degrees. For this study, graduating versus not graduating
is an example of a quasi-independent variable.
51. The participants in a research study are classified as high, medium, or low in self-esteem.
This classification involves measurement on a nominal scale.
52. A discrete variable must be measured on a nominal or an ordinal scale.
53. Classifying people into two groups on the basis of gender is an example of measurement
on an ordinal scale.
54. Students in an introductory art class are classified as art majors and non-art majors. This is
an example of measurement on a nominal scale.
55. To determine how much difference there is between two individuals, you must use either
an interval or a ratio scale of measurement.
56. If a researcher measures two individuals on a nominal scale, it is impossible to
determine which individual has the larger score.
57. If a researcher measures two individuals on an ordinal scale, then it is impossible to
determine how much difference exists between the two people.

Instructor Notes - Chapter 1 - page 12


58. For statistical purposes, there usually is not much difference between scores from an
interval scale and scores from a ratio scale.
59. Recording the number of students who are absent each day at a high school would be
an example of measuring a discrete variable.
60. A high school gym teacher records how much time each student requires to complete a onemile run. This is an example of measuring a continuous variable.
61. In an introductory theater class, the professor records each student’s favorite movie from the
previous year. The teacher is measuring a discrete variable.
62. A data set is described as consisting of n = 15 scores. Based on the notation being used, the

data set is a sample.
2

63. To compute (ΣX) , you first add the scores, then square the total.
64. The first step in computing Σ(X + 1), is to add 1 point to each score.
2

2

65. For the following scores, X = (X) .

Scores: 1, 1, 1, 1

66. For the following scores, Σ(X + 1) = 9.

Scores: 1, 3, 0, 1

2

67. For the following scores, Σ(X + 1) = 81. Scores: 1, 3, 0, 1
68. For the following scores, Σ(X – 1) = 10. Scores: 1, 3, 7
2

69. For the following scores, ΣX = 35 . Scores: 1, 3, 5
2

70. For the following scores, ΣX = 49. Scores: 1, 4, 2, 0

Other Exam Items
71. Statistical techniques are classified into two major categories: Descriptive and Inferential.

Describe the general purpose of each category.
72. Define the concept of "sampling error." Note: Your definition should include the concepts
of sample, population, statistic, and parameter.

Instructor Notes - Chapter 1 - page 13


73. (www) Describe the sequence of mathematical operations that would be used to evaluate
each of the following expressions.
2
a. ΣX
2
b. (ΣX)
c. ΣX – 2
d. Σ(X – 2)
2
e. Σ(X – 2)
74. Calculate each value requested for the following set of scores. Scores: 1, 2, 0, 4
a. ΣX
2
b. ΣX
2
c. (ΣX)
75. Calculate each value requested for the following set of scores. Scores: 5, 2, 4, 2
a. ΣX – 2
b. Σ(X – 2)
2
c. Σ(X – 2)
76. Calculate each value requested for the following set of scores.
a. ΣX

X Y
b. ΣY
1 5
c. ΣXΣY
3 1
d. ΣXY
0 –2
2 –4
Answers for Multiple-Choice Questions (with section and page numbers from the text)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.

c, 1.2, p.
d, 1.2, p.
b, 1.2, p.
a, 1.2, p.
d, 1.2, p.
a, 1.2, p.
a, 1.2, p.
c, 1.2, p.
b, 1.2, p.
b, 1.2, p.

5
6
7
6
7
6
7
7
7
7

11.
12.
13.
14.
15.
16.
17.
18.
19.
20.

c, 1.2, p. 8
a, 1.3, p. 16
c, 1.3, p. 16
d, 1.3, p. 12
a, 1.3, p. 16
c, 1.3, p. 18
d, 1.3, p. 16

b, 1.4, p. 21
c, 1.4, p. 21
b, 1.4, p. 21

21.
22.
23.
24.
25.
26.
27.
28.
29.
30.

b, 1.4, p. 23
b, 1.4, p. 23
c, 1.4, p. 24
d, 1.4, p. 24
d, 1.4, p. 24
b, 1.5, p. 27
d, 1.5, p. 28
c, 1.5, p. 29
d, 1.5, p. 28
b, 1.5, p. 28

31.
32.
33.
34.

35.
36.
37.
38.
39.
40.

a, 1.5, p. 29
d, 1.5, p. 28
a, 1.5, p. 29
d, 1.5, p. 28
b, 1.5, p. 29
d, 1.5, p. 28
a, 1.5, p. 28
b, 1.5, p. 29
b, 1.5, p. 28
c, 1.5, p. 28

Answers for True/False Questions (with section and page numbers from the text)
41. F, 1.2, p.
42. T, 1.2, p.
43. F, 1.2, p.

8
5
7

51. F, 1.4, p. 23
52. F, 1.4, p. 21
53. F, 1.4, p. 23

61. T, 1.4, p. 21
62. T, 1.5, p. 27
63. T, 1.5, p. 28

Instructor Notes - Chapter 1 - page 14


44.
45.
46.
47.
48.
49.
50.

F, 1.2, p. 7
T, 1.3, p. 14
F, 1.3, p. 13
T, 1.3, p. 13
T, 1,3, p. 13
F, 1.3, p. 16
T, 1.3, p. 18

54.
55.
56.
57.
58.
59.

60.

T, 1.4, p. 23
T, 1.4, p. 24
T, 1.4, p. 23
T, 1.4, p. 24
T, 1.4, p. 25
T, 1.4, p. 21
T, 1.4, p. 21

64.
65.
66.
67.
68.
69.
70.

T, 1.5, p. 28
F, 1.5, p. 28
T, 1.5, p. 28
F, 1.5, p. 29
F, 1.5, p. 28
T, 1.5, p. 28
F, 1.5, p. 28

Answers for Other Exam Items
71. The purpose of descriptive statistics is to simplify the organization and presentation of
data. The purpose of inferential statistics is to use the limited data from a sample as the basis for
making general conclusions about the population.

72. A parameter is a value that is obtained from a population of scores and is used to describe
the population. A statistic is a value obtained from a sample and used to describe the sample.
Typically it is impossible to obtain measurements for an entire population, so researchers must
rely on information from samples; that is, researchers use statistics to obtain information about
unknown parameters. However, samples provide only limited information about their
populations. Thus, sample statistics are usually not identical to their corresponding population
parameters. The error or discrepancy between a statistic and the corresponding parameter is
called sampling error.
2

To compute ΣX , you first square each score, then sum the squared values.
2
To compute (ΣX) , you first sum the scores, then square the sum.
To compute ΣX  2, you first sum the scores, then subtract 2 from the sum.
To compute Σ(X – 2) you first subtract 2 from each score, then sum the resulting
values.
2
e. To compute Σ(X – 2) , you first subtract 2 from each score, then square the
resulting values, then sum the squared numbers.

73.

a.
b.
c.
d.

74.

a. 7

b. 21
2
c. (7) = 49

75.

a. 11
b. 5
c. 13

76.

a.
b.
c.
d.

6
0
0
0
Instructor Notes - Chapter 1 - page 15