In a completely randomized design, 10 experimental units were used for the first
ID: 3331200 • Letter: I
Question
In a completely randomized design, 10 experimental units were used for the first treatment, 12 for the second treatment, and 19 for the third treatment. Sum of Squares due to Treatments and Sum of Squares Total is computed as 1100 and 1700 respectively. Prepare the ANOVA table and complete the same (fill out all the cells).
a.) State the Hypotheses.
b.) At a .05 level of significance, is there a significant difference between the treatments?
c.) Use both p-Value and Critical-Value approaches.
Please tell me exactly what to type into Excel and if there are any formulas that can be used to get this answer. Thanks so much.
Explanation / Answer
Sol:
a)
H0: µ1 = µ2 = µ3 (All treatments have the same mean responses)
Ha: Not all Treatments means are equal (At least one of the three treatments has a different mean than others)
Source of Variation
Sum of Squares
d.f.
Mean Squares
F
P-value
Treatments
Error
Total
1100
600
1500
2
38
40
550
15.79
34.83
0.0000000025
3.2448
b)
nT = 10 + 12 + 19 = 41
Total d.f. = 41 -1 = 40
Treatments d.f. = 3-1 = 2
Alpha = 0.05
C)
P-value approach: p-value = 0.0000000025 < Alpha = 0.05. Reject H0. At least one of the treatments has a significantly different mean than the rest
Critical-value approach: test statistic F = 34.83 > Critical value = F0.05, 2, 38 = 3.2448. Reject H0. At least one of the treatments has a significantly different mean than the rest
Yes, there are significant differences between the treatment means.
Source of Variation
Sum of Squares
d.f.
Mean Squares
F
P-value
Treatments
Error
Total
1100
600
1500
2
38
40
550
15.79
34.83
0.0000000025
3.2448