The analysis of variance for a randomised complete block design produced the ANOVA table entries shown below.
Source
SS
Df
MS
F
Treatments
27.1
3
(e)
(g)
Blocks
(a)
5
14.90
(h)
Residuals
33.4
(c)
(f)
Total
(b)
(d)
Give the alternative hypothesis appropriate to test for the difference between the treatments.
None of the above
The alternative hypothesis appropriate to test for the difference between the treatments would be:
"H1: There is a significant difference between at least two treatment means."
To determine the alternative hypothesis appropriate to test for the difference between the treatments in the analysis of variance (ANOVA) table, we need to understand the components in the table.
The ANOVA table in a randomised complete block design typically consists of the following components:
- Source: The source of variation in the experiment, in this case, "Treatments", "Blocks", and "Residuals".
- SS: The sum of squares.
- Df: The degrees of freedom.
- MS: The mean square.
- F: The F-value.
However, in the given table, some of the entries are missing and marked as (a), (b), (c), (d), (e), (f), (g), and (h).
To determine the alternative hypothesis, we need to know the values in the table that are missing, particularly the MS for "Treatments" and "Residuals", and the F-value. Without these values, it is not possible to determine the alternative hypothesis correctly.
Therefore, based on the given information, it is not possible to provide an alternative hypothesis appropriate to test for the difference between the treatments.
The alternative hypothesis to test for the difference between the treatments in the analysis of variance for a randomised complete block design would be:
H₁: At least one treatment mean is different from the others.