2. Three types of fertilizer are to be tested to see which one yields more corn

Question

2. Three types of fertilizer are to be tested to see which one yields more corn crop. Forty similar plots of land were available for testing purposes. The 40 plots are divided at random into four groups, ten plots in each group. Fertilizer 1 was applied to each of the ten corn plots in Group 1. Similarly, Fertilizers 2 and 3 were applied to the plots in Groups 2 and 3, respectively. The corn plants in Group 4 were not given any fertilizer; it will serve as the control group. The attached file P147.txt' gives the corn yield yij for each of the forty plots. (a) Create three indicator variables F1, F2, F3, one for each of the three fertilizer groups (b) Fit the model yij wo A Fil Aus F12 Au3Fi3 Eij. (c) Which of the three fertilizers has the greatest effects on corn yield? (d) Test the hypothesis that, on the average, none of the three types of fertilizer has an effect on corn crops. Specify the hypothesis to be tested, the test used, and your conclusions at the 5% significance level.

Explanation / Answer

a. F1 = 1 when fertilizer 1 is added, for the first 10 observations

Similarly, F2=1 for next 10 observations and F3=1 for next 10 observations

b. The regression equation obtained is :

b. Y = 29.8 + 6.8F1 + 0.1F2 + 5.1F3

c. So, most significant slope is for fertilizer 1 and it has the highest impact on crop yield

d. We see the 2 tailed pa values to check if fertilizer coefficients are equal to 0 or not.

Hence, we see that the p values as obtained from regression are 0.001, 0.9635, 0.0242. So, at the 5% level we see tht coefficients for fertilizer 1 and 3 are significant but not for 2

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