WEEK 5 – EXERCISES Enter your answers in the spaces provided. Save the file using your last name as the beginning of the file name (e.g., ruf_week5_exercises) and submit via “Assignments.” When appropriate, show your work . You can do the work by hand, scan/take a digital picture, and attach that file with your work. For the following question(s): A school counselor tests the level of depression in fourth graders in a particular class of 20 students. The counselor wants to know whether the kind of students in this class differs from that of fourth graders in general at her school. On the test, a score of 10 indicates severe depression, while a score of 0 indicates no depression. From reports, she is able to find out about past testing. Fourth graders at her school usually score 5 on the scale, but the variation is not known. Her sample of 20 fifth graders has a mean depression score of 4.4. Use the .01 level of significance. 1. The counselor calculates the unbiased estimate of the population’s variance to be 15. What is the variance of the distribution of means? A) 15/20 = 0.75 B) 15/19 = 0.79 C) 15 2 /20 = 11.25 D) 15 2 /19 = 11.84 2. Suppose the counselor tested the null hypothesis that fourth graders in this class were less depressed than those at the school generally. She figures her t score to be - .20. What decision should she make regarding the null hypothesis? A) Reject it B) Fail to reject it C) Postpone any decisions until a more conclusive study could be conducted D) There is not enough information given to make a decision 3. Suppose the standard deviation she figures (the square root of the unbiased estimate of the population variance) is .85. What is the effect size? A) 5/.85 = 5.88 B) .85/5 = .17 C) (5 - 4.4)/.85 = .71 D) .85/(5 - 4.4) = 1.42 For the following question(s): Professor Juarez thinks the students in her statistics class this term are more creative than most students at this university. A previous study found that students at this university had a mean score of 35 on a standard creativity test. Professor Juarez finds that her class scores an average of 40 on this scale, with an estimated population standard deviation of 7. The standard deviation of the distribution of means comes out to 1.63. 4. What is the t score? A) (40 - 35)/7 = .71 B) (40 - 35)/1.63 = 3.07 C) (40 - 35)/7 2 = 5/49 = .10 D) (40 - 35)/1.63 2 = 5/2.66 = 1.88 5. What effect size did Professor Juarez find? A) (40 - 35)/7 = .71 B) (40 - 35)/1.63 = 3.07 C) (40 - 35)/7 2 = 5/49 = .10 D) (40 - 35)/1.63 2 = 5/2.66 = 1.88 6. If Professor Juarez had 30 students in her class, and she wanted to test her hypothesis using the 5% level of significance, what cutoff t score would she use? (You should be able to figure this out without a table because only one answer is in the correct region.) A) 304.11 B) 1.699.

1. WEEK 5 – EXERCISES
Enter your answers in the spaces provided. Save the file using
your last name as the beginning of the file name (e.g.,
ruf_week5_exercises) and submit via “Assignments.” When
appropriate,
show your work
. You can do the work by hand, scan/take a digital picture, and
attach that file with your work.
For the following question(s): A school counselor tests the level
of depression in fourth graders in a particular class of 20
students. The counselor wants to know whether the kind of
students in this class differs from that of fourth graders in
general at her school. On the test, a score of 10 indicates severe
depression, while a score of 0 indicates no depression. From
reports, she is able to find out about past testing. Fourth graders
at her school usually score 5 on the scale, but the variation is
not known. Her sample of 20 fifth graders has a mean
depression score of 4.4. Use the .01 level of significance.
1.
The counselor calculates the unbiased estimate of the

2. population’s variance to be 15. What is the variance of the
distribution of means?
A)
15/20 = 0.75
B)
15/19 = 0.79
C)
15
2
/20 = 11.25
D)
15
2
/19 = 11.84
2.
Suppose the counselor tested the null hypothesis that fourth
graders in this class were
less
depressed than those at the school generally. She figures her
t

3. score to be
-
.20. What decision should she make regarding the null
hypothesis?
A)
Reject it
B)
Fail to reject it
C)
Postpone any decisions until a more conclusive study could be
conducted
D)
There is not enough information given to make a decision
3.
Suppose the standard deviation she figures (the square root of
the unbiased estimate of the population variance) is .85. What is
the effect size?
A)

4. 5/.85 = 5.88
B)
.85/5 = .17
C)
(5
-
4.4)/.85 = .71
D)
.85/(5
-
4.4) = 1.42
For the following question(s): Professor Juarez thinks the
students in her statistics class this term are more creative than
most students at this university. A previous study found that
students at this university had a mean score of 35 on a standard
creativity test. Professor Juarez finds that her class scores an
average of 40 on this scale, with an estimated population
standard deviation of 7. The standard deviation of the
distribution of means comes out to 1.63.
4.
What is the
t
score?
A)

5. (40
-
35)/7 = .71
B)
(40
-
35)/1.63 = 3.07
C)
(40
-
35)/7
2
= 5/49 = .10
D)
(40
-
35)/1.63
2
= 5/2.66 = 1.88
5.
What effect size did Professor Juarez find?

6. A)
(40
-
35)/7 = .71
B)
(40
-
35)/1.63 = 3.07
C)
(40
-
35)/7
2
= 5/49 = .10
D)
(40
-
35)/1.63
2
= 5/2.66 = 1.88
6.

7. If Professor Juarez had 30 students in her class, and she wanted
to test her hypothesis using the 5% level of significance, what
cutoff
t
score would she use? (You should be able to figure this out
without a table because only one answer is in the correct
region.)
A)
304.11
B)
1.699
C)
-
.113
D)
-
2.500
For the following question(s): A school counselor claims that he

8. has developed a technique to reduce prestudying procrastination
in students. He has students time their procrastination for a
week and uses this as a pretest (before) indicator of
procrastination. Students then attend a workshop in which they
are instructed to do a specific warming-up exercise for studying
by focusing on a pleasant activity. For the next week, students
again time their procrastination. The counselor then uses the
time from this week as the posttest (after) measure.
7.
Suppose the counselor wants to examine whether there is a
change of any kind (either an increase or decrease) in
procrastination after attending his workshop. What would be the
appropriate description of “Population 2” (the population to
which the population his sample represents is being compared)?
A)
People whose posttest scores will be lower than their pretest
scores
B)
People whose change scores will be greater than 0
C)
People whose change scores will be 0
D)
People whose change scores will be less than their pretest

9. scores
8.
Presume the counselor wants to examine whether there is a
change (either an increase or decrease) in procrastination after
attending his workshop. If the counselor tests 10 students using
the .05 level of significance, what cutoff
t
score(s) will he use? (You should be able to figure this out
without a table.)
A)
-
2.62, 0, +2.62
B)
+2.262
C)
-

10. 2.262, 0
D)
-
2.262, +2.262
9.
Suppose the counselor found the sum of squared deviations
from the mean of the sample to be 135. Given that he tested 10
people, what would be the estimated population variance?
A)
135/10 = 13.5
B)
135/9 = 15.0
C)
10/135 = .074
D)
9/135 = .067

11. 10.
A researcher conducts a study of perceptual illusions under two
different lighting conditions. Twenty participants were each
tested under both of the two different conditions. The
experimenter reported: “The mean number of effective illusions
was 6.72 under the bright conditions and 6.85 under the dimly
lit conditions, a difference that was not significant,
t
(19) = 1.62.”
Explain this result to a person who has never had a course in
statistics. Be sure to use sketches of the distributions in your
answer.

12. SPSS ASSIGNMENT #5
Single Sample & Dependent Samples t Tests
SPSS instructions: (For more details, check the links provided
under “Course Materials” in the Course Overview Folder (under
Lessons).
t Test for a Single Sample:
Open SPSS
Enter the number of activities of daily living performed by the
depressed clients studied in #1 in the Data View window.
In the Variable View window, change the variable name to
“ADL” and set the decimals to zero.
Click Analyze
à
Compare Means
à

13. One-Sample T test
à
the arrow to move “ADL” to the Variable(s) window.
Enter the population mean (14) in the “Test Value” box.
Click OK.
t Test for Dependent Means:
Open SPSS
Enter the number of activities of daily living performed by the
depressed clients studied in Problem 2 in the Data View
window. Be sure to enter the “before therapy” scores in the first
column and the “after therapy” scores in the second column.
In the Variable View window, change the variable name for the
first variable to “ADLPRE” and the variable name for the
second variable to “ADLPOST”. Set the decimals for both
variables to zero.
Click Analyze
à
Compare Means
à
Paired-Samples T Test
à
the arrow to move “ADLPRE” to the Paired Variable(s) window
à
“ADLPOST” and then click the arrow to move the variable to
the Paired Variable(s) window.

14. Click OK.
Review the five steps of hypothesis testing and complete the
following problems. Be sure to cut and past the appropriate
result boxes from SPSS under each problem.
Researches are interested in whether depressed people
undergoing group therapy will perform a different number of
activities of daily living after group therapy. The researchers
have randomly selected 12 depressed clients to undergo a 6-
week group therapy program.
Use the five steps of hypothesis testing to determine whether
the average number of activities of daily living (shown below)
obtained after therapy is significantly different from a mean
number of activities of 14 that is typical for depressed people.
(Clearly indicate each step).
Test the difference at the .05 level of significance and, for
practice, at the .01 level (in SPSS this means you change the
“confidence level” from 95% to 99%).
In Step 2, show all calculations.

15. As part of Step 5, indicate whether the behavioral scientists
should recommend group therapy for all depressed people based
on evaluation of the null hypothesis at both levels of
significance and calculate the effect size.
CLIENT
AFTER THERAPY
A
17
B
15
C
12
D
21
E
16
F
18
G
17
H
14
I
13
J
15
K
12
L
19

16. Researchers are interested in whether depressed people
undergoing group therapy will perform a different number of
activities of daily living before and after group therapy. The
researchers have randomly selected 8 depressed clients in a 6-
week group therapy program.
Use the five steps of hypothesis testing to determine whether
the observed differences in numbers of activities of daily living
(shown below) obtained before and after therapy are
statistically significant at the .05 level of significance and, for
practice, at the .01 level. (Clearly indicate each step).

17. In Step 2, show all calculations. As part of Step 5, indicate
whether the researchers should recommend group therapy for all
depressed people based on evaluation of the null hypothesis at
both levels of significance and calculate the effect size.
CLIENT
BEFORE THERAPY
AFTER THERAPY
A
12
17
B
7
15
C
10
12
D
13
21
E
9
16
F
8
18
G
14
17
H
11
8