Question

2. Three types of ferilizer 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, 10 plots in Group 1. Similarly, Fertilizers 2 and 3 were applied to the plots in Group 2 and 3, respectively. The corn plants in Group 4 were not given any fertilizer; it will serve as the control group. Table 2 gives the corn yield yij for each of the 40 plots. Please answer the following questions. You may use R or other program language if needed. (a) Create three indicator variables F1,F2,F3, one for each of the three fertilizer groups. (b) Fit the model yij = Ho + HiFi + H2F2+H3Fi3 + tij. (c) 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. (d) Test the hypothesis that, on the average, none of the three types of fertilizer have equal effects on corn crop but different from that of the control group. Specify the hypothesis to be tested, the test used, and your conclusions at the 5% significance level. (e) Which of the three fertilizers has the greatest effects on corn yield?

use the R or by hand.

Answer 1

> fl=c(31, 34, 34, 34,43,35,38,36,36,45) > f2=C(27,27,25,34,21,36,34,30,32,33) > f3=C(36,37,37,34,37,28,33,29,36,42) > control=C(33,27,35,25,29,20,25,40,35,29) > reg=1m(control-f1+f2+f3) > summary(reg) Call: Im(formula = control – f1 + f2 + f3) Residuals: Min 10 Median -6.6461 -4.0755 -0.8601 30 Max 2.1668 10. 3151 Coefficients: Estimate std. Error t value Pr>t (Intercept) 51. 51973 30.40458 1.694 0.141 fi -0.186390 .56387 -0.331 0.752 f2 -0.53262 0.49901 -1.067 0.327 f3 0.02944 0.64011 0.046 0.965 Residual standard error: 6.534 on 6 degrees of freedom Multiple R-squared: 0.1984, Adjusted R-squared: -0.2024 F-statistic: 0.4951 on 3 and 6 DF, p-value: 0.6989 > #Fitted model as Control=51.51973-0.18639*fertilizer 1-0.53262*fertilizer 2+0.02944*fertilizer 3 > #sice p value of the fi,f2 and f3 are not less than 0.05 from the t test we cannot reject Ho > #Hence we can say that the fertilizers are not having significant relation on the control > #Performed the ANOVA test here to find the claim of none of the fertilizers have any impact on the control > #Ho: mul=mu2=mu3=0 > #since p value of the entire test is 0.6989 which is not less than 0.05 we cannot rejetc Ho > #Hence we can say that all the fertilizers combined are not having significant relation on the control #The highest coefficient is of f2 which is -0.53262 and hence we can say that fertilizer 2 has the maximum impact on the controll Ictic Motor

Done the above analysis in R.

#R code for copy paste below

f1=c(31,34,34,34,43,35,38,36,36,45)
f2=c(27,27,25,34,21,36,34,30,32,33)
f3=c(36,37,37,34,37,28,33,29,36,42)
control=c(33,27,35,25,29,20,25,40,35,29)
reg=lm(control~f1+f2+f3)
summary(reg)

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