Final Answer:
The ANOVA results suggest a statistically significant difference in mean production yields at different temperatures (F(2,6) = 6.75, p < 0.05). Therefore, we reject the null hypothesis and conclude that temperature has a significant effect on the average production yield.
Step-by-step explanation:
To perform the analysis of variance (ANOVA), we first calculate the sum of squares (SS) for each source of variation. The total sum of squares (SST) is obtained by summing the squared deviations of each data point from the overall mean. The sum of squares between groups (SSB) is computed by summing the squared deviations of each group mean from the overall mean, weighted by the number of observations in each group. The sum of squares within groups (SSW) represents the variability within each group and is calculated by summing the squared deviations of individual data points from their respective group means.
Degrees of freedom (df) are then determined for each source of variation. The degrees of freedom between groups (dfB) is equal to the number of groups minus 1, and the degrees of freedom within groups (dfW) is equal to the total number of observations minus the number of groups. Mean squares (MS) for each source of variation are obtained by dividing the sum of squares by the degrees of freedom.
The F-statistic is calculated by dividing the mean square between groups by the mean square within groups. In this case, the F-statistic of 6.75 exceeds the critical value at a 0.05 significance level, leading to the rejection of the null hypothesis. Thus, we can conclude that temperature significantly influences the average production yield in the chemical process.