The Analysis of Variance. A research study compared beer consumed daily between 3 groups with 3 observations each. Group1 was UCB, Group 2 UCSD, and Group 3 UCI. Determine if there is a significant difference among the groups 5% level.
Group1: UCB
Group 2: UCSD
Group 3: UCI
The Results of this study are in the following table:
Group1 Group2 Group3
Sample 3, 4, 5 3.2, 4, 4.2 3, 4, 3.3
Mean 4.0 3.7 3.4
S^2 4.4 5.2 6.1
null and alternative hypotheses are
Null hypothesis Ho
:
There is a significant difference among the treatment group means
Alternative Hypothesis Ha
: At least one group mean is different from other group means
the average mean due to treatments are
Thus, the average mean due to treatments is 3.67
the Treatment Sum Square SSTR is
Thus, the Treatment Sum Square (SSTR) is 0.550
The Mean Square Treatments MSTR
Mean Square Treatments (MSTR) is 0.275
Based on MSTR and Mean Squared Error MSE = 4.5 should we reject Ho? Please use F table with 2 numerator df, 6 denominator df, alpha =0.05