Question

Please Use only R studio to produce the output and boxplots for this problem

Fertilizers A biology student is studying the effect of 10 different fertilizers on the growth of mung bean sprouts. She sprouts 12 beans in each of 10 different petri dishes, and adds the same amount of fertilizer to each dish. After one week she measures the heights of the 120 sprouts in millimeters. Here are boxplots and an ANOVA table of the data: 140 HO Heights (mm) H HTH ILLIUILL HTH A B C D G H I J E F Fertilizer Source DF Sum of Squares Mean Square F-Ratio P-Value Fertilizer 9 2073.708 230.412 1.1882 0.3097 Error Total 110 119 21331.083 193.919 23404.791

Answer 1

Here, we are testing the effect of fertilizers on the growth of sprouds using ANOVA table and boxplots.

a). For the complete ANOVA model,

Ho : The growth of mung bean sprouts is independent of use of fertilizers or there is no significant effect of fertilizers on the growth of mung bean sprouts. or $\mu$ i = 0 for all i = 0, ...., 10 where $\mu$ i is the mean effect of ith fertilizer

H1: The growth of mung bean sprouts is dependent of use of fertilizers or there is significant effect of fertilizers on the growth of mung bean sprouts or $\mu$ i $\neq$ 0 for atleast 1 i where i = 0 , ...., 10

b). From the anova table we can see that the p-value corresponding to the Fertiizers = 0.3097 which speaks of its non significance in the model. Since, we know we reject Ho when p-value < level of significance ( 0.1, or 0.05 or 0.01), here we fail to reject Ho. or can say that the Growth of mung bean sprouts is independent of the use of fertilisers.

c). Here, to check the comparison between each of the fertilizers, we carry post-hoc analysis but since the entire model is not significance we do not compare fertilizers.

Also, in this case, Ho : The 10 fertilizers have equal effect on growth of sprouts or the growth of sprouts is independent of the type of fertilizer or $\mu$ i = $\mu$ j where i = 0,...,10 and j =0, ...10 but i $\neq$ j.

And, since there is no data given for me to perform the post hoc or the output given to interpret it. I cant help further.

Please rate my answer and feel free to comment for doubts.