Choose the one alternative that best completes the statement or answers the question.
-Four different watering schedules are used on bean plants. The number of beans on each randomly selected plant is given below. Use the Kruskal-Wallis test to find the test statistic H to test the hypothesis that there is no difference in the distribution of the populations. Use $\alpha = 0.05$.
$\begin{array}{cccc}
\hline \text { Schedule } 1 & \text { Schedule } 2 & \text { Schedule } 3 & \text { Schedule 4 } \
\hline 9 & 8 & 9 & 6 \
8 & 11 & 6 & 8 \
9 & 8 & 7 & 6 \
10 & 8 & 6 & 7 \
10 & 8 & 5 & 8 \
9 & 9 & 6 & 7
\end{array}$

A) $12.833$
B) $10.922$
C) $15.364$
D) $14.818$

Question

Choose the one alternative that best completes the statement or answers the question.
-Four different watering schedules are used on bean plants. The number of beans on each randomly selected plant is given below. Use the Kruskal-Wallis test to find the test statistic H to test the hypothesis that there is no difference in the distribution of the populations. Use $\alpha = 0.05$.
$\begin{array}{cccc}
\hline \text { Schedule } 1 & \text { Schedule } 2 & \text { Schedule } 3 & \text { Schedule 4 } \
\hline 9 & 8 & 9 & 6 \
8 & 11 & 6 & 8 \
9 & 8 & 7 & 6 \
10 & 8 & 6 & 7 \
10 & 8 & 5 & 8 \
9 & 9 & 6 & 7
\end{array}$

A) $12.833$
B) $10.922$
C) $15.364$
D) $14.818$

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 population distributions are identical without assuming them to follow the normal distribution.To calculate the Kruskal-Wallis test statistic $H$, you first rank all the data from all groups together; then, for each group, you sum the ranks and use them in the formula for $H$. The formula for $H$ is:$$H = \left( \frac{12}{N(N+1)} \right) \sum \frac{R_i^2}{n_i} - 3(N+1)$$where $N$ is the total number of observations across all groups, $n_i$ is the number of observations in group $i$, $R_i$ is the sum of ranks in group $i$, and the summation is over all groups.Given the data, after ranking all observations and calculating the sum of ranks for each schedule, and then applying the formula, the test statistic $H$ is found to be approximately $12.833$, which matches choice A. This calculation involves detailed steps including ranking all the data points from 1 to the highest, calculating the sum of ranks for each group, and then applying these sums in the formula.

Choose the One Alternative That Best Completes the Statement or Answers