1. **State the problem:** We are given data on fertilizers with equal variance and need to solve questions 2 to 7 related to variance estimation and ANOVA. 2. **Estimate the population variance from the variance between the means of columns:** The variance between column means estimates the variance of the population means. 3. **Estimate the population variance from the variance between the samples of columns:** This estimates the within-group variance (error variance). 4. **Test the hypothesis that the population means are the same at 5% significance level:** Use ANOVA to test $H_0: \mu_1=\mu_2=\mu_3=\mu_4$ against $H_a$: not all means equal. 5. **Find SSA, SSE, SST, degrees of freedom, MSA, MSE, and F-ratio:** - $SSA = \sum n_i(\bar{X}_i - \bar{X})^2$ (Sum of Squares Among groups) - $SSE = \sum \sum (X_{ij} - \bar{X}_i)^2$ (Sum of Squares Error) - $SST = SSA + SSE$ (Total Sum of Squares) - Degrees of freedom: $df_{A} = k-1$, $df_{E} = N-k$, $df_{T} = N-1$ - Mean Squares: $MSA = \frac{SSA}{df_A}$, $MSE = \frac{SSE}{df_E}$ - F-ratio: $F = \frac{MSA}{MSE}$ 6. **Construct ANOVA table:** | Source | SS | df | MS | F | |--------|----|----|----|---| | Among | SSA | $k-1$ | MSA | F | | Error | SSE | $N-k$ | MSE | | | Total | SST | $N-1$ | | | 7. **Conduct ANOVA and draw conclusions:** - Compare calculated $F$ with critical $F$ at 5% level. - If $F_{calc} > F_{crit}$, reject $H_0$; otherwise, fail to reject. **Note:** Without the original data table, exact numerical answers cannot be computed here. Please provide the data table to perform calculations.