For this problem, my task is simple. I have to be able to "summarize what key concepts are being explained in the example. I have to summarize what the problem is explaining and the bottom-line concepts described in the problem."

Can you help me summarize what this problem is stating and be able to explain it in basic English? Thank you.

The applications of statistics to crop studies, which began in the 19205, frequently makes use of a particular blocking variable, the plot. As farmers have long known, dif- ferent plots of land have unique combinations of water, sunlight, and soil chemicals, each having a signicant effect on crop growth and yield. Oranges, for example, are so sensitive to different amounts of sunlight that it is a well-known fact that the sweet- est oranges come from the south side of the tree.2 In a study of different rootstocks for orange trees, four different varieties of rootstock are tested by planting each variety on the same ten plots of land.3 The numbers of oranges produced by these trees are recorded in Figure 9.11. In this study, the factor A = \"variety\" has a = 4 levels. The blocking factor B = \"plot\" has I) = 10 levels. Block (plot) 1 2 3 4 5 6 '1' 8 9 10 Average: Inanunnnuuaum anamnnnnnnnlw Treatment wasnannnnnannlu 4annnnnnannlm Average: 12.25 13.0 10.5 10.25 10.75 9.75 11.0 11.25 11.25 13.5 Figure 9.1 I Number of oranges per tree (in 1005) for Example 9.6 The grand average of the 40 values is J? = 11.4, and the AN OVA calculations for this data are as follows: SSTr = 1320?, if i=1 =10[(10.' >(x;; - x)2 i=1j=1 = (11 - 11.4)+ (12 - 11.4) + (10 - 11.4)2 + ... + (11 - 11.4)- + (14 - 11.4) = 113.6 By subtraction, SSE = SST - SSTr - SSB = 113.6 - 58.2 - 49.1 = 6.3. All of this information is summarized in the ANOVA table: Source of variation df SS MS F Treatments (variety) a - 1 = 3 58.2 19.4 83.15 Blocks (plots) b - 1 = 9 49.1 5.456 23.38 Error (a - 1)(b - 1) = 27 6.3 2333 Total variation ab - 1 = 39 113.6 Using a significance level of a a = .05, we can conclude that the different va- rieties do have different mean yields since F = MSTr/ MSE = 83.15 has a P-value smaller than .05. We can also conclude that the different plots have differing effects on yield since F = MSB/MSE = 23.38 also has a P-value smaller than .05, although this conclusion only confirms our original belief about the effect of different plots. When Ho is rejected, Tukey's method can be applied to identify significant dif- ferences among treatments