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) 152/20 = 11.25
D) 152/19 = 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)/72 = 5/49 = .10
D) (40 35)/1.632 = 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)/72 = 5/49 = .10
D) (40 35)/1.632 = 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.
1. A psychotherapist studied whether his clients self-disclosed more while sitting in an easy chair or lying down on a couch. All clients had previously agreed to allow the sessions to be videotaped for research purposes. The therapist randomly assigned 10 clients to each condition. The third session for each client was videotaped and an independent observer counted the clients’ disclosures. The therapist reported that “clients made more disclosures when sitting in easy chairs (M = 18.20) than when lying down on a couch (M = 14.31), t(18) = 2.84, p < .05, two-tailed.” Explain these results to a person who understands the t test for a single sample but knows nothing about the t test for independent means.
2. A researcher compared the adjustment of adolescents who had been raised in homes that were either very structured or unstructured. Thirty adolescents from each type of family completed an adjustment inventory. The results are reported in the table below. Explain these results to a person who understands the t test for a single sample but knows nothing about the t test for independent means.
Means on Four Adjustment Scales for
Adolescents from Structured versus Unstructured Homes
Scale Structured Homes Unstructured Homes t
Social Maturity 106.82 113.94 –1.07
School Adjustment 116.31 107.22 2.03*
Identity Development 89.48 94.32 1.93*
Intimacy Development 102.25 104.33 .32
______________________
*p < .05
3. Do men with higher levels of a particular hormone show higher levels of assertiveness? Levels of this hormone were tested in 100 men. The top 10 and the bottom 10 were selected for the study. All participants took part in a laboratory simulation in which they were asked to role-play a person picking his car up from a mechanic’s shop. The simulation was videotaped and later judged by independent raters on each of four types of assertive statements made by the participant. The results are shown in the table below. Explain these results to a person who fully understands the t test for a single sample but knows nothing about the t test for independent means.
Mean Number of Assertive Statements
Type of Assertive Statement
Group 1 2 3 4
Men with High Levels 2.14 1.16 3.83 0.14
Men with Low Levels 1.21 1.32 2.33 0.38
t 3.81** 0.89 2.03* 0.58
______________________
*p < .05; **p < 0.1
4. A manager of a small store wanted to discourage shoplifters by putting signs around the store saying “Shoplifting is a crime!” However, he wanted to make sure this would not result in customers buying less. To test this, he displayed the signs every other Wednesday for 8 weeks, for a total of 4 days displayed. He recorded the store’s sales for those four Wednesdays and then recorded the store’s sales for the four alternate Wednesdays, when the signs were not displayed. On the Wednesdays with the sign, the sales were 83, 73, 81, and 79. On the Wednesdays without the sign, sales were 84, 90, 82, and 84.
Do these results suggest that customers buy less when the signs are displayed? (Use the .05 significance level.)
a. Use the five steps of hypothesis testing.
b. Sketch the distribution involved.
c. Figure the effect size.
d. Explain what you did to a person who is familiar with the t test for a single sample but is unfamiliar with the t test for independent means.
1. A sports researcher gave a standard written test of eating habits to 12 randomly selected professionals, four each from baseball, football, and basketball. The results were as follows:
Eating Habits Scores
Baseball Players Football Players Basketball Players
34 27 35
18 28 44
21 67 47
65 42 61
Is there a difference in eating habits among professionals in the three sports? (Use the .05 significance level.)
a. Use the five steps of hypothesis testing.
b. Sketch the distribution involved.
c. Determine effect size.
2. A team of psychologists designed a study in which 12 psychiatric patients diagnosed as having generalized anxiety disorder were randomly assigned to one of three new types of therapy, here labeled X, Y, and Z. One year after therapy, the patients’ overall mental health scores were as follows:
Mental Health Assessment
Therapy X Therapy Y Therapy Z
85 78 79
79 81 83
84 68 75
67 75 74
Do these results suggest that the different therapies have different effects on mental health?
(Use the .05 level.)
a. Use the five steps of hypothesis testing.
b. Sketch the distribution involved.
c. Explain your results.
1. A researcher plans a study in which a crucial step is offering participants a food reward. It is important that the three food rewards be equal in appeal. Thus, a prestudy was designed in which participants were asked which of the rewards they preferred. Of the 60 participants, 16 preferred cupcakes, 26 preferred candy bars, and 18 favored dried apricots. Do these scores suggest that the different foods are differentially preferred by people in general? (Use the .05 significance level.)
a. Use the five steps of hypothesis testing.
b. Sketch the distribution involved.
c. Explain your findings.
2. A high school principal wanted to know if the racial makeup of her teachers mirrored that of the student body. The student body broke down into 47% White, 28% Latino, 15% African American, and 10% other. Of the 65 teachers, 42 were White, 4 were Latino, 15 were African American, and 4 were Other. Do these results suggest that the racial makeup of the faculty members is different from that of the students? (Use the .05 significance level.)
Use the five steps of hypothesis testing and explain your findings.