Homework 5
Z-Scores
Be sure you have reviewed this module/week’s lessons and
presentations along with the practice data analysis before proceeding to the
homework exercises. Complete all analyses in SPSS, and then copy and paste your
output and graphs into your homework document file. Number all responses.
Answer any written questions (such as the text-based questions or the APA
Participants section) in the appropriate place within the same file. Review the
“Homework Instructions: General” document for an example of how homework
assignments must look.

Part I: Concepts
These
questions are based on the Nolan and Heinzen reading and end-of-chapter
questions.

1.
What are always the mean and standard deviation of the z-distribution?
2. Define
the central limit theorem.
3. Fill
in the blanks: A z-score is based on a distribution of _____________, while a z-statistic
is based on a distribution of __________________.
4. End-of-chapter
problems: Remember to show work to receive partial credit where applicable. For
help working on these problems, refer to the presentation from this module/week
on the normal curve and computing z-scores.
·
Raw and z-scores: 6.16 and 6.20
·
Estimating
percentages under normal curve: 6.27
·
Distribution of means and z-statistic: 6.28 and 6.30

Part II: SPSS Analysis
1. Green
and Salkind, Lesson 21, Exercise 1
Open the “Lesson 21 Exercise File 1” document
(found in the course’s Assignment Instructions folder) in order to complete
these exercises.
a.
Create a histogram of the anxiety raw scores and paste it
b.
Using the descriptives method covered in the
presentation and chapter, transform the anxiety raw scores to z-scores,
creating a new variable called “z_anxiety.” Paste the output of descriptive
statistics in your homework document. These descriptive statistics should
describe the original raw scores and not the new z scores.
c.
Remember that the mean of a standard normal
distribution is z = 0 and the standard deviation is 1. What is the z-score that
is closest to 0 (on either side of the mean) in your data set? What is the z-score
that is the farthest from 0 (on either side of the mean) in your data set?

d.
Based on the histogram from (a) and the answers to (c),
would you describe the anxiety data as being normally distributed? Why or why
regarding normal and standard normal z-distributions.

Part III: SPSS Data
Entry and Analysis
1.
The following data represent IQ scores of a sample of
30 high school students. In the general population, IQ scores have a mean of
100 and a standard deviation of 15.

IQ Scores

123
119
104
145
108
100
115
105
60
122
105
87
98
124
80

93
89
123
118
104
112
96
85
98
105
91
113
82
124
90

a.
Generate descriptive statistics and a histogram for
this variable. Based on the data and graph, choose
1 measure of central tendency and 1 measure of dispersion (variability) that
best describes the data set. Justify why you chose these measures in a statement beneath the output.
b.
In your data set, standardize the IQ scores by
transforming them into z-scores under a new variable “ZIQ.” Using your data set
as a reference, what z-score corresponds to a raw IQ score of 115? To a raw IQ
score of 60? To a raw IQ score of 104?
c.
Based on what you have been told about IQ scores in the
beginning of the problem, does this sample’s distribution seem to reflect the
distribution of IQ scores in the general population? Why or why not?

Part IV: Cumulative
1.
(Non-SPSS) A cognitive psychologist wants to find out
whether playing Minecraft® affects fourth graders’ scores on a visuospatial
task. He assigns 30 fourth graders to 1 of 2 groups. Group 1 plays Minecraft®
for 20 minutes, then completes the visuospatial task. Group 2 completes the
a.
What is the independent variable in this experiment?
b.
What is the dependent variable?
c.
What is the likely null hypothesis for this experiment?
d.
What is the likely research hypothesis for this
experiment?

2.
(Non-SPSS) A clinical psychologist wants to test a new
long-term treatment program for people diagnosed with bipolar disorder. She
assigns 20 participants to the new treatment program and 20 participants to a
standard treatment program.
a.
State the likely null hypothesis for this study.
b.
State the likely research hypothesis for this study.

3.
(SPSS) A criminal psychologist wants to examine the
level of narcissistic personality traits between those who are diagnosed with antisocial
personality disorder (ASPD) and those who do not qualify for ASPD. She
administers a measure of narcissistic personality traits where higher scores
indicate higher levels of narcissism and scores range from 0–35.

ASPD Diagnosis

No ASPD Diagnosis

23
11
19
21
22
9
16
27
31
31

10
8
19
13
6
4
9
15
11
7

a.
Create a new SPSS data file for these scores. Your file
must have 2 variables: diagnosis and score. Your diagnosis variable must be set
up as a 1-column grouping variable with 2 groups (diagnosis, no diagnosis)
coded numerically. This will be much like the gender variable you created in a
previous module/week. For example, if you code ASPD Diagnosis as 1 and No ASPD
Diagnosis as 2, then the SPSS file will appear somewhat like the following:

Column 1

Column 2

“Diagnosis”

“Score”

1

23

1

11

1

19

All ASPD Diagnosis scores from the
table above will appear in a similar fashion.
Then, enter No ASPD Diagnosis information as:

2

10

2

8

2

19

Continue in this fashion to the end of
the file.
b. Compute
descriptive statistics by diagnosis (that is, for each of the two groups in one
table) using similar steps to those covered in Green and Salkind’s Lesson 21
and in the Module/Week 3 presentation (HS GPA scores by Gender). Paste this into
c. Construct
a boxplot to show the difference between the mean scores of the 2 groups.

Submit Homework 5 by 11:59 p.m. (ET) on Monday of
Module/Week 5.

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