The following data were obtained for a randomized block design involving five treatments and three blocks: SST = 490, SSTR = 310, SSBL = 95. Set up the ANOVA table. (Round your value for F to two decimal places, and your p-value to three decimal places.)
Source of Variation |
Sum of Squares |
Degrees of Freedom |
Mean Square |
F | p-value |
---|---|---|---|---|---|
Treatments | |||||
Blocks | |||||
Error | |||||
Total |
Test for any significant differences. Use α = 0.05.
State the null and alternative hypotheses.
H0: At least two of the population means are
equal.
Ha: At least two of the population means are
different.H0: μ1 =
μ2 = μ3 =
μ4 = μ5
Ha: μ1 ≠
μ2 ≠ μ3 ≠
μ4 ≠
μ5 H0:
Not all the population means are equal.
Ha: μ1 =
μ2 = μ3 =
μ4 =
μ5H0:
μ1 = μ2 =
μ3 = μ4 =
μ5
Ha: Not all the population means are
equal.H0: μ1 ≠
μ2 ≠ μ3 ≠
μ4 ≠ μ5
Ha: μ1 =
μ2 = μ3 =
μ4 = μ5
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to three decimal places.)
p-value =
State your conclusion.
Do not reject H0. There is sufficient evidence to conclude that the means of the treatments are not all equal.Reject H0. There is not sufficient evidence to conclude that the means of the treatments are not all equal. Reject H0. There is sufficient evidence to conclude that the means of the treatments are not all equal.Do not reject H0. There is not sufficient evidence to conclude that the means of the treatments are not all equal.
Source | SS | df | MS | F | p value |
treatments | 310 | 4 | 77.50 | 7.29 | 0.009 |
blocks | 95 | 2 | 47.50 | 4.47 | 0.050 |
error | 85 | 8 | 10.63 | ||
total | 490 | 14 |
H0: μ1 = μ2 = μ3 = μ4 = μ5
Ha: Not all the population means are equal
value of the test statistic =7.29
p value =0.009
Reject H0. There is sufficient evidence to conclude that the means of the treatments are not all equal.
The following data were obtained for a randomized block design involving five treatments and three blocks:...
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