Question

. Many people believe that having more money will make them happy. Dr. Shakespeare designed an experiment in which he randomly and evenly assigned 15 people to three groups. He gave one group nothing, gave the second group a little money, and gave the third group a lot of money. The next day, he asked each group to report their happiness on a mood scale (0-100 with a higher score indicating happier mood). The first group reported an average of 80, the second 90, and the third group 85. Using the SS total provided in the following table to examine if the amount of money has an effect on the perceived happiness (make sure to fill out the ANOVA table). If yes, how? (14pts)

Source	SS	df	MS	F
Factor A	___	___	___	____
Error	___	___	___
Total	500	___

Answer 1

Given: Number of groups, k = 3 and N = 15

M1 = 80, M2 = 90 and M3 = 85

Overall Mean = (80 + 90 + 85) / 3 = 255/3 = 85

SS A = SUM(n * [Mean - Overall Mean]² = 5 * (90 - 85)² + 5 * (85 - 85)² + 5 * (85 - 85)² = 250

SS Total = SSA + SSerror

Therefore SS Error = SS Total - SSA = 500 - 250 = 250

DF A = k - 1 = 3 - 1 = 2

DF Error = N - k = 15 - 3 = 12

DF Total = DF A + DF Error = 2 + 12 = 14

MS A = SSA / DF A = 250/2 = 125

MS Error = SS Error/DF error = 250/12 = 20.83

F Stat = MS A / MS error = 125 / 20.83 = 6

The Complete ANOVA Table is as below

Source	SS	DF	MS	F
A	250	2	125	6
Error	250	12	20.83
Total	500	14

The Hypothesis:

H0: There is no effect on the groups on the amount of money ()

Ha: There is an effect on the amount of money (At least one of is different from the others)

The Test Statistic: From the ANOVA Table, the Fstatistic = 6

Critical Value: = 0.05 (default), DFA = 2 and DF error = 14, the critical value is 3.8853

The p value: For Fstat = 6, DFA = 2 and DF error = 14, the pvalue = 0.0156

The Decision Rule: If F Stat is > Critical Value, Then Reject H0.

Also if p value is < , Then reject H0

The Decision: Since F Stat (6) is > F Critical (3.8853), We Reject H0.

Also since p value (0.0156) is < (0.05), we reject H0.

The Conclusion: There is sufficient evidence at the 95% significance level to conclude that there is an effect of amount of money on perceived happiness. i.e as the amount of money increases the perceived happiness also increases.