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) 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.

9.

10.

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

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

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

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