Assignment 14: One-tailed Tests and Assumptions
Psych 6250
Spring, 2010
Story Problem: the mean level of depression of some population of people who have
recently experienced the loss of a pet has been found to equal 65. A researcher would
like to know if participating in a support group affects (raises or lowers) the level of
depression. Thirty nine people who had recently experienced the loss of a pet
participated in a support group, their level of depression was measured after their
participation and the (fictional) data are given in the file “Depression.sav”. On this
measure lower scores reflect less depression, higher scores greater depression.
We will begin by analyzing the data using a two-tailed test.
1. State H0 for the analysis:__________
2. State HA for the analysis:__________
Analyze the data using SPSS. Go to Analyze>>Compare Means>>One-Sample T Test
menu. Put the variable into the Test Variable(s) box, and for the ‘Test Value’ input the
value for the population mean proposed by H0.
3. What was the mean level of depression in the sample?__________
4. What is the probability that we would have obtained a sample mean that far from
what H0 predicted if only chance were involved?__________ (don’t round off)
5. Draw a curve and shade in the areas that represent the p value.
6, 7, and 8.. Report the results of the analysis in the form t(...)=...., p=......
9. What is your decision regarding H0?
a. Reject H0
b. Do not reject H0
10. What is your decision regarding the level of depression in the population of people
who participate in the support group?
a. Can conclude it is different than what H0 proposes.
b. Cannot determine whether it is different than what H0 proposes.
11. Can you conclude that it was participation in the support group that actually caused
depression to be different?
a. Yes, because we rejected H0.
b. No, because we didn’t reject H0.
c. No, we only know the mean is different, something else might have caused the
difference.
Now analyze the data to test a theory which says that the support group should
specifically lower the level of depression.
12. State H0 for the analysis:__________
13. State HA for the analysis:__________
14. What is the probability that we would have obtained a sample mean that far below
what H0 predicted if only chance were involved?__________ (don’t round off).
15. Draw a curve and shade in the areas that represent the p value.
16. What is your decision regarding H0?
a. Reject H0
b. Do not reject H0
17. What is your decision regarding the level of depression in the population of people
who participate in the support group?
a. Can conclude it is lower than what H0 proposes.
b. Cannot determine whether it is lower than what H0 proposes.
Now analyze the data to test a theory which says that the support group should
specifically raise the level of depression.
18. State H0 for the analysis:__________
19. State HA for the analysis:__________
20. What is the probability that we would have obtained a sample mean that far above
what H0 predicted if only chance were involved?__________
21. Draw a curve and shade in the areas that represent the p value.
22. What is your decision regarding H0?
a. Reject H0
b. Do not reject H0
23. What is your decision regarding the level of depression in the population of people
who participate in the support group?
a. Can conclude it is higher than what H0 proposes.
b. Cannot determine whether it is higher than what H0 proposes.
24. Let’s go back to the two-tailed test. We can conclude that the population mean is
different that what H0 proposed. The sample mean is lower than what H0 proposed. The
odds that the actual population mean is also specifically lower than what H0 proposed are
_______ to 1.
25. State the p value you would use to determine whether or not the difference between
the mean of the population and what H0 proposes is in the same direction as the sample
mean._________ (don’t round)
26. The p value from the question above should be compared to ______ (numeric value)
to see if it is statistically significant.
27. Can we conclude that the mean of the population is lower than what H0 proposes?
(yes/no).
28. Which of the following are assumptions that underlie the t test for a single group
mean? (circle all that apply).
a. The scores are dependent
b. The scores are independent
c. The population is normally distributed
d. The population is not normally distributed.
e. The mean is meaningful.
29. How important is the assumption regarding independence/dependence?
a. Not very important, the test is ‘robust’ in this regard.
b. Quite important, this should not be violated