2. (Coding) The sample dataset (crop.csv) from our imaginary crop yield experiment contains data about: fertilizer: fertilizer type (type 1, 2, or 3) density: planting density (1 = low density, 2 = high density) block: planting location in the field (blocks 1, 2, 3, or 4) yield: final crop yield (in bushels per acre). Perform the following tasks using Python. 1. Use the two sample F-test to check whether the two types of density result in the same variance of yield at significance level a = 0.05. 2. Based on your conclusion in Part 1, perform a suitable two-sample T-test to check whether the two types of density result in the same mean of yield at significance level a = 0.05. 3. We now compare the effect of different fertilizer on the yield. (a) Plot the three QQ-plots of the yield under the three choices of fertilizer. Argue whether you can regard them as following a normal distribution. (b) Plot the three boxplots of the yield under the three choices of fertilizer. Argue whether you can regard them as having the same variance. (c) Perform the Bartlett's test to check whether the three different fertilizer gives the same variance in the yield. (d) Perform ANOVA to check if the three fertilizer gives the same mean in the yield. (e) Perform two-sample T-test with Bonferroni adjustment to identify the pairs of fertilizer give significantly different mean in the yield. (f) For post-hoc analysis, use the Tukey's HSD test to find the pair(s) of fertilizer give significantly different mean in the yield. Compare the result with Part (e). 4. (Optional) Repeat Part 3 with block and yield. N 6 N 2 3 4 1 density block 2 1 3 2 4 1 5 2 6 1 7 2 8 1 9 2 10 1 11 2 12 1 13 2 14 1 15 16 1 17 2 18 1 19 2 20 1 21 2 22 1 23 2 24 1 25 2 26 1 fertilizer yield 1 1 177.2287 1 177.55 3 1 176.4085 4 1 177.7036 1 1 177.1255 2 1 176.7783 3 1 176.7463 4 1 177.0612 1 1 176.2749 2 1 177.9672 3 1 176.6013 4 1 177.03051 1 1 177.4795 2 1 176.8741 3 1 176.1144 4 1 176.0084 1 1 176.1083 2 1 178.3574 3 1 177.2624 4 1 176.9188 1 1 176.239 1 176.5731 3 1 176.03931 4 1 176.8179 1 1 176.1606 N - N