30. A psychologist would like to know whether the change in seasons has any consistent effect on people's mood. In the middle of each of the four seasons, the psychologist selects a random sample of n = 20 students. Each individual in these four separate samples is given a standardized mood/depression questionnaire. The data from this study were examined using an analysis of variance and the results are shown in the summary table below.

Fill in all the missing values in the table (questions 30-41). [Hint: You don't have to answer #30-36 in order; in fact, it may be easiest to start with #36.]

Source SS df MS F

Between Treatments _____ ____ 20 4.00

Within Treatment _____ ____ ____

Total _____ ____

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Compute SS_between

31. Compute SSwithin

32. Compute SSTotal

33. Compute dfBetween

34. Compute dfwithin

35. Compute dftotal

36. Compute MSWithin

37. Which of the following correctly represents the null and alternative hypothesis (MUST SHOW WORK FOR THIS PROBLEM)?

a. H₀:11=22=33 = 44

H₁: at least one is different

b. H₀: x₁= x₂= x₃ = x₄

H₁: at least one xis different

c. H₀: at least one xis different

H₁:x₁= x₂= x₃= x₄

d. H₀: at least oneis different

H₀:11=22=33=44

38. Compute F-crit(MUST SHOW WORK FOR THIS PROBLEM). Use alpha = .05

39. Compute F-obs.(MUST SHOW WORK FOR THIS PROBLEM)

Hint:look at question 30...

40. Based on the calculated test statistic,would you reject the null hypothesis established in question 37(MUST SHOW WORK FOR THIS PROBLEM)?

a. yes

b. no

41. Based on the previously conducted steps,we canconcludethat(MUST SHOW WORK FOR THIS PROBLEM):

a. There is a significant difference in mood based on season

b. There is no significant difference in mood based on season

c. Participants were more depressed in winter compared to the other seasons

d. Cannot make a conclusion without the actual data