An ANOVA test is used to see if there are significant differences in yield due to different catalysts, comparing a calculated F-statistic to a critical F-value at a 5% significance level.
To determine whether the difference in yield due to the use of different catalysts is significant, we perform an ANOVA (Analysis of Variance) test. Since the problem statement gives the yields for the four catalysts across three different plants, we would typically structure an ANOVA table to calculate the sums of squares within groups (catalysts), between groups (plants), and the total sum of squares. The calculated F-statistic from the ANOVA table is compared with the critical F-value (F3,6 = 4.76 for a 5% significance level) to determine if there is a statistically significant difference in yield due to the different catalysts.
The calculation of the ANOVA involves steps such as computing the means for each group, the grand mean, the sum of squares due to treatment (between-groups), the sum of squares within groups, and the total sum of squares. Then degrees of freedom for each are determined, along with mean squares, which involve dividing the respective sums of squares by their associated degrees of freedom. Finally, the F-statistic is calculated by dividing the mean square due to treatment by the mean square within groups.
If the calculated F-value exceeds 4.76, we can conclude that there are significant differences in yield due to the catalysts. Otherwise, we would conclude that the yield differences are not statistically significant at the 5% level.
The question probably maybe:
a chemical firm wants to determine how four catalysts differ in yield. the firm runs the experiment in three plants, types a, b, and c. in each plant, the yield is measured with each catalyst. the yield (in quintals) is as follows :
plant catalyst
1 2 3 4
a 2 1 2 4
b 3 2 1 3
c 1 3 3 1
perform an anova and comment on whether the yield due to a particular catalyst is significant or not at a 5% significance level. we were given f3,6 = 4.76.