In a two-way ANOVA experiment, factor A is operating on 3 levels, factor B is operating on 2 levels, and there are 2 replications per cell. If MSA/MSE = 5.35, and MSB/MSE = 5.72, and MSAB/MSE = 6.75 and using the 0.05 level of significance, what conclusions would be reached regarding the respective null hypotheses for this experiment?

To determine the conclusions regarding the respective null hypotheses for this two-way ANOVA experiment, we need to compare the calculated F-values with the critical F-value at the chosen level of significance (0.05).

The null hypotheses for a two-way ANOVA are as follows:
1. Null hypothesis for factor A (Main effect of A): There is no significant difference among the means of the levels of factor A.
2. Null hypothesis for factor B (Main effect of B): There is no significant difference among the means of the levels of factor B.
3. Null hypothesis for the interaction of A and B (Interaction effect): There is no significant interaction between the levels of factors A and B.

To test these hypotheses, we calculate F-values based on the mean square values (MSA, MSB, MSAB) and the mean square error (MSE).

The calculated F-values are obtained by dividing the mean square values (MSA, MSB, MSAB) by the mean square error (MSE). Therefore, in this case:
- F-value for factor A: F_A = MSA/MSE = 5.35
- F-value for factor B: F_B = MSB/MSE = 5.72
- F-value for interaction: F_AB = MSAB/MSE = 6.75

Comparing these calculated F-values with the critical F-value at the chosen significance level (0.05), we can conduct the following tests:

1. Main effect of factor A:
Using the F-distribution table or statistical software, we compare F_A with the critical F-value for factor A. If F_A is greater than the critical F-value, we reject the null hypothesis for factor A, indicating that there is a significant difference among the means of the levels of factor A.

2. Main effect of factor B:
Similarly, we compare F_B with the critical F-value for factor B. If F_B is greater than the critical F-value, we reject the null hypothesis for factor B, indicating that there is a significant difference among the means of the levels of factor B.

3. Interaction effect of A and B:
Again, we compare F_AB with the critical F-value for the interaction effect. If F_AB is greater than the critical F-value, we reject the null hypothesis for the interaction effect, indicating that there is a significant interaction between the levels of factors A and B.

To reach the conclusions regarding these null hypotheses, you need to obtain the critical F-values at the 0.05 significance level and compare them with the respective calculated F-values (F_A, F_B, F_AB).