Four different types of fertilizers are used on raspberry plants. The number of raspberries on each randomly selected plant is given below. Use the Kruskal-Wallis test to find the test statistic H to test the claim that there
Is no difference in the distribution of the populations. $$\begin{array} { c c c c }
\hline \text { Fertilizer 1 } & \text { Fertilizer 2 } & \text { Fertilizer 3 } & \text { Fertilizer 4 } \
\hline 11 & 10 & 11 & 8 \
10 & 13 & 8 & 10 \
11 & 10 & 9 & 8 \
12 & 10 & 8 & 9 \
12 & 10 & 7 & 10 \
11 & 11 & 8 & 9 \
\hline
\end{array}$$
A)12.833
B)10.922
C)15.364
D)14.818

Question

Four different types of fertilizers are used on raspberry plants. The number of raspberries on each randomly selected plant is given below. Use the Kruskal-Wallis test to find the test statistic H to test the claim that there
Is no difference in the distribution of the populations. $$\begin{array} { c c c c } 
\hline \text { Fertilizer 1 } & \text { Fertilizer 2 } & \text { Fertilizer 3 } & \text { Fertilizer 4 } \
\hline 11 & 10 & 11 & 8 \
10 & 13 & 8 & 10 \
11 & 10 & 9 & 8 \
12 & 10 & 8 & 9 \
12 & 10 & 7 & 10 \
11 & 11 & 8 & 9 \
\hline
\end{array}$$
A)12.833
B)10.922
C)15.364
D)14.818

Quizplus · Accepted Answer

The Kruskal-Wallis test statistic is calculated as:H = (12/n(n+1)) * Σ(Rj - R)^2where n is the total number of observations, Rj is the sum of the ranks in the jth group, and R is the overall mean rank.In this case, n = 24, R1 = 66, R2 = 60, R3 = 42, R4 = 48, and R = (66+60+42+48)/4 = 54.Therefore, H = (12/24(24+1)) * ((66-54)^2 + (60-54)^2 + (42-54)^2 + (48-54)^2) = 12.833.The critical value for the Kruskal-Wallis test with 3 degrees of freedom and a significance level of 0.05 is 7.815. Since H > 7.815, we reject the claim that there is no difference in the distribution of the populations.

Four Different Types of Fertilizers Are Used on Raspberry Plants