## Psychology 280 Exam 2 Study Guide

Psychology 280 Exam 2 Study Guide

1. What is a standard error? How does it relate to a standard deviation?

2. What does a z for a sample mean represent? How does a z differ from a t?

3. What is the difference between ? and s?

4. How do you calculate the standard error of the mean (i.e. a single mean) if you know

?? How do you calculate the standard error of the mean if you don’t know ??

5. What is the effect of n on the standard error of the mean?

6. What is a null hypothesis? What is an alternative hypothesis?

7. Why are hypotheses written in terms of population parameters and not sample

statistics?

8. If the null hypothesis is true, what percent of sample means will fall within +/- 1.96

standard errors of the mean? What percent will fall within +/- 2 standard errors of the

mean? What percent will fall within +/- 2.58 standard errors and between +/- 3.30

standard errors?

9. If the null hypothesis is true, what percent of sample means will be greater than 1.96

standard errors of the mean? What percent will be lower than 1.96 standard errors?

10. What does alpha refer to?

11. When doing hypothesis testing, why do researchers typically use alphas of .05, .01,

or .001?

12. What is a Type I error, and how does it relate to the alpha level?

13. What is a Type II error, and how does it relate to a Type I error?

14. How do I decrease my probability of making a Type I error? When I decrease my

probability of making a Type I error, what happens to my probability of making a Type

II error? How can I decrease Type I and Type II errors simultaneously?

15. What does it mean to say that a result is “statistically significant”?

16. What does it mean to say that a result is “not significant”?

17. What are the assumptions of a single sample z-test? What are some examples of

violations of each of the assumptions?

18. Why is it important to evaluate “practical significance” in addition to “statistical

significance”?

19. What does Cohen’s d assess? What are the cutoffs for “small”, “medium”, and “large”

effects, according to Cohen’s d?

20. What is the difference between a one sample t-test and a one sample z-test? When

would we perform a z-test, and when would we do a t-test instead?

21. What are degrees of freedom?

22. Why do we have to use degrees of freedom for a t-test?

23. What are the values given in a t-table? What do they represent?

24. How do you use a t-table to decide if a sample mean differs significantly from a

population mean?

25. What are the assumptions of a single sample t-test?

26. What does r2 evaluate? What are the cutoffs for deciding whether an effect is

“small”, “medium”, or “large” according to the r2 value?

27. What are the differences between a single sample t-test and a two-sample t-test?

28. Why do we have two sources of error when calculating the standard error for a two

sample t-test?

29. Be able to calculate M1, M2, n1, n2, df1, df2, SS1, SS2, s1

2, s2

2, s1, s2, sp

2, sM, s(M1-M2), sMD,

t, z, d, and r2. Be able to describe what each of these values represents.

30. Be able to calculate the standard error of the mean, assuming you know ?. Be able to

calculate the standard error of the mean, assuming you don’t know ?.

31. Be able to perform a single sample z-test, starting from raw data.

32. Be able to perform a single sample t-test, starting from raw data.

33. Be able to perform a two sample t-test, starting from raw data.

34. Be able to perform a repeated measures t-test, starting from raw data.

35. Be able to calculate sp

2 for a two samples t-test.

36. Why do we use a pooled variance for the two sample t-test?

37. What are the differences between a Between-Subjects design and a Within-Subjects

design? Which type of t-test is appropriate for each?

38. What are the primary advantages of a Within-Subjects design?

39. What are the disadvantages of a Within-Subjects design?

40. What is a Difference Score? How are difference scores used in a Within-Subjects

design?

41. What are “order effects”? What is “counterbalancing”?

42. What is a critical t? What is a critical region? What is an obtained t?

43. What is homogeneity of variance?

Psychology 280 Exam 2 Study Guide

Sample Questions:

1. What happens to the standard error of the mean as n decreases?

a. it increases

b. it decreases

c. it stays the same

d. none of the above

2. Assume a researchers wishes to compare a sample mean from one group with a known

population mean. Assume the researcher also knows the value of the standard

deviation of scores in the population. Which analysis should be performed?

a. single sample t-test

b. single sample z-test

c. independent samples t-test

d. repeated measures t-test

3. What goes into the denominator of a t-test?

a. observed mean difference

b. population mean

c. sample size

d. standard error

4. Assume a researcher conducts a one-sample z-test, and obtains a z = 1.52. Assume she

wants to use a conventional level for ?. Can she reject HO ?

a. no

b. yes

c. yes, if she decreases alpha

d. yes, if she increases alpha

5. Which of the following is a null hypothesis? a. M1 = M2

b. µ = 50

c. µ ? 100

d. D ? 0

6. Which of the following is the symbol for the null hypothesis?

a. HO

b. HA

c. µ

d. ?

7. Which of the following make it more likely that a researcher can reject a null

hypothesis?

a. increase n

b. increase s

c. use a large d

d. use more groups

8. A medical researcher is working on a new treatment for a certain type of cancer. The

average survival time in the population, after diagnosis, is two years using the

standard treatment. After trying a new treatment on three patients, she observes an

average survival time of four years. Even though survival has doubled, the result is

not statistically significant at the .05 level. Which of the following is the most likely

explanation for the non-significant result?

a. survival time has not really increased

b. the sample was too small to detect a significant difference

c. the effect size is too large

d. a lower alpha level should have been used

9. If we reject a null hypothesis when it is true, what kind of error have we made?

a. Type I

b. Type II

c. none – we haven’t made an error

d. choosing an alpha that is too low

10. A researcher fails to reject a null hypothesis that is false. What happened?

a. A Type I error

b. A Type II error

c. She used an alpha that was too high

d. She made the correct decision

11. Which of the following will increase the “power” of a statistical test?

a. Increase the probability of a Type II error

b. Reject HO only if the obtained t exceeds the critical t

c. increase n

d. use a better significance test

12. A new diet is developed to decrease cholesterol levels in adults at risk of developing

heart disease. The mean cholesterol level in the patient population is 200. A sample

of 50 patients tries the new diet, and after 3 months, the mean cholesterol is M = 192,

with s = 21.

12A. What type of statistical test should be performed?

a. single sample z-test

b. single sample t-test

c. independent samples t-test

d. repeated measures t-test

12B. What are the degrees of freedom for this test?

a. 21

b. 49

c. 51

d. 191

12C. What is the critical t, assuming ? = .05?

a. 1.96

b. 2.02

c. 2.58

d. 1.68

12D. What is the obtained t?a. 3.42

b. 2.89

c. -2.69

d. -2.89

12E. What statistical conclusion should the researcher make?

a. reject HO

b. retain HO

c. use a larger n

d. the result is not statistically significant

13. Which of the following is an example of a repeated measures design?

a. a teacher compares pre-test and post-test scores for a sample of students

b. a teacher compares the learning scores of two different groups of students

c. a teacher compares the learning scores of her students with the population

mean

d. a teacher compares the pre-test and post-test scores for two matched samples

of students

14. A researcher is interested in whether coaching can increase IQ scores. It is known

that the mean IQ in the population is 100, with a standard deviation of 15. A sample

of 36 participants is randomly chosen, and provided with the coaching program. After

the program, the mean IQ in this sample is 115. The researcher wishes to perform a

statistical test to see if the coaching had an effect.

14A. What type of test should be performed?

a. Single sample z-test

b. Single sample t-test

c. Independent samples t-test

d. Repeated measures t-test

14B. What is the null hypothesis?

a. µ = 115

b. µ = 100

c. µ ? 100

d. M = 100

14C. What are the degrees of freedom for this test?

a. 35

b. 36

c. 100

d. Degrees of freedom don’t apply because we are doing a z-test

Psychology 280 Exam 2 Study Guide

14D. What is the critical value that we use for testing the null hypothesis, with ? = .

05?

a. 2.02

b. 2.58

c. 3.30

d. 1.96

14E. What is the standard error of the mean?

a. 2.5

b. 15

c. 6

d. Cannot be determined from the information given

14F. What is the obtained value of the test statistic (z or t)?

a. 6.0

b. 2.5

c. 15

d. 115

14G. What should the researcher conclude?

a. Reject HO

b. Retain HO

c. HA has been proven

d. The coaching has no effect

14H. What is the value of Cohen’s d?

a. 15

b. 1.0

c. 2.0

d. 6.0

14I. Is the observed effect small, medium, or large, according to Cohen’s criteria?

a. Small

b. Medium

c. Large

d. Cannot be determined from the information given

15. A researcher is interested in whether coaching improves scores on a test used for

selecting graduate students in Psychology. The test has a mean in the population of

50. A sample of 10 students participate in the coaching, and then take the test. Their

scores are: 53, 57, 61, 49, 52, 56, 58, 62, 51, 56.

15A. What is the sample mean?

a. 10

b. 50

c. 55.5

d. 56.5

15B. What type of statistical test should be performed to evaluate whether the

coaching was effective?

a. Single sample z-test

b. Single sample t-test

c. Independent samples t-test

d. Repeated measures t-test

15C. What are the degrees of freedom for the appropriate statistical test?

a. 10

b. 9

c. 8

d. 50

15D. Which of the following is the null hypothesis?

a. µ = 50

b. µ ? 50

c. M = 50

d. HA

15E. What is the critical value for the appropriate statistical test, assuming ? = .05?

a. z = 1.96

b. t = 2.262

c. t = 2.228

d. t= 1.833

15F. What are the Sums of Squares in the treatment group?

a. 55.50

b. 18.06

c. 162.50

d. 4.25

15G. What is the variance in the treatment group?

a. 55.50

b. 18.06

c. 162.50

d. 4.25

15H. What is the standard deviation in the treatment group?

a. 55.50

b. 18.06

c. 162.50

d. 4.25

15I. What is the standard error of the mean?

a. 4.10

b. 7.37

c. 4.25

d. 1.34

Psychology 280 Exam 2 Study Guide

15J. What is the value of the test statistic (z or t)?

a. 1.96

b. 7.37

c. 1.34

d. 4.10

15K. What should the researcher conclude?

a. Reject HO

b. Retain HO

c. HA has been proven

d. The coaching has no effect

15L. What is the value of Cohen’s d?

a. 50

b. 4.25

c. 1.29

d. 2.05

15M. Is the observed effect small, medium, or large, according to Cohen’s criteria

for d?

a. Small

b. Medium

c. Large

d. Cannot be determined from the information given

15N. What is the value of the r2?

a. .65

b. .42

c. .86

d. .82

15O. Is the observed effect small, medium, or large, according to Cohen’s criteria

for r2?

a. Small

b. Medium

c. Large

d. Cannot be determined from the information given

16. Assume a researcher conducts a study of the effects of a new cognitive behavior

therapy method designed to reduce anxiety. A group of anxious patients is identified,

and some of them are randomly assigned to a control group which receives no

treatment, while the others receive the new therapy. After the treatment, the

anxiety levels are obtained using a standardized test of trait anxiety. The scores are

given below. Conduct the appropriate statistical test (using ? = .05), and indicate

which of the following conclusions is justified. SHOW YOUR WORK, INCLUDING: n’s,

df’s, s’s, sp

2, M’s, standard error, obtained t, critical t.

Control Group Treatment Group

X f X f

6 1 3 1

7 2 4 1

8 1 7 2

9 1 9 1

10 1

12 1

13 1

a. There is no difference between those who received the therapy and those who did

not

b. Those who received the therapy had reported significantly lower anxiety than

those who did not

c. HO is true

d. HA has been proven

17. What is the value of Cohen’s d for the example described in #16 above?

a. 1.21

b. 6.18

c. 2.42

d. .31

18. Assume a researcher is interested the effects of a new cognitive behavior therapy

method designed to reduce anxiety. A group of anxious patients is identified. Prior to

treating the patients, their anxiety levels are recorded. The new therapy is

administered, and then the anxiety levels of the patients are measured again. The

scores are given below. Conduct the appropriate statistical test (using ? = .05), and

indicate which of the following conclusions is justified. SHOW YOUR WORK,

INCLUDING: n’s, df’s, s’s, s2, standard error, M’s, obtained t, critical t.

Participant Before Treatment After Treatment

A 8 7

B 9 2

C 6 4

D 7 5

E 6 5

F 8 3a. There is no difference between those who received the therapy and those who

did not

b. Those who received the therapy had reported significantly lower anxiety than

those who did not

c. HO is true

d. HA has been proven

19. What is the value of Cohen’s d for the study described in Item #18 above?

a. 6.0

b. 3.0

c. 1.98

d. 1.22

20. What is the value of the r2 for the study described in Item #18 above?

a. .64

b. .25

c. 1.22

d. cannot be determined from the information given