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 critical value H to test the claim that there
Is no difference in the distribution of the populations. Use $$\alpha$$ = 0.05. $$\begin{array} { c c c c }
\hline \text { Fertilizer 1 } & \text { Fertilizer 2 } & \text { Fertilizer 3 } & \text { Fertilizer 4 } \
\hline 11 & 10 & 11 & 8 \
10 & 13 & 8 & 10 \
11 & 10 & 9 & 8 \
12 & 10 & 8 & 9 \
12 & 10 & 7 & 10 \
11 & 11 & 8 & 9 \
\hline
\end{array}$$
A)7.815
B)7.352
C)6.531
D)5.198

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 critical value H to test the claim that there
Is no difference in the distribution of the populations. Use $$\alpha$$ = 0.05. $$\begin{array} { c c c c } 
\hline \text { Fertilizer 1 } & \text { Fertilizer 2 } & \text { Fertilizer 3 } & \text { Fertilizer 4 } \
\hline 11 & 10 & 11 & 8 \
10 & 13 & 8 & 10 \
11 & 10 & 9 & 8 \
12 & 10 & 8 & 9 \
12 & 10 & 7 & 10 \
11 & 11 & 8 & 9 \
\hline
\end{array}$$
A)7.815
B)7.352
C)6.531
D)5.198

Quizplus · Accepted Answer

The Kruskal-Wallis test is a non-parametric method for testing whether samples originate from the same distribution. It is used for comparing more than two samples that are independent, or not related. The hypothesis being tested is whether the populations from which the samples originate have the same median. The critical value for the Kruskal-Wallis test depends on the number of groups and the degrees of freedom, which is the number of groups minus one. Given that there are four groups (four types of fertilizers) and using a significance level of $\alpha = 0.05$, the degrees of freedom is $4 - 1 = 3$. Looking up the critical value for $3$ degrees of freedom in a chi-square ($\chi^2$) distribution table at $\alpha = 0.05$, we find the critical value to be $7.815$. This is the value used to decide if the observed test statistic is in the rejection region, which would indicate a significant difference between the groups.

Four Different Types of Fertilizers Are Used on Raspberry Plants α\alphaα

Four Different Types of Fertilizers Are Used on Raspberry Plants $\alpha$