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
C) –.113
D) –2.500
For the following question(s): A school counselor claims that he 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 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) –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
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.
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 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 àPaired-Samples T Test àthe 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.
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.
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 |
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).
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 |