A researcher tests three different brands of $2 \%$ milk to see how many grams of fat are in e 8 ounce glass. The results are shown below along with the sums of the ranks of the differ brands.
$\begin{array}{ccc}
\hline \text { Brand A } & \text { Brand B } & \text { Brand C } \
\hline 4.68 & 4.64 & 4.70 \
4.66 & 4.67 & 4.68 \
4.64 & 4.68 & 4.71 \
4.71 & 4.66 & 4.69 \
4.67 & 4.69 & 4.70 \
\hline
\end{array}$

$$\boldsymbol { R } _ { \mathbf { A } } = 33 ; \boldsymbol { R } _ { \mathbf { B } } = 29 ; \boldsymbol { R } _ { \mathbf { C } } = 58$$ What is the test value for the Kruskal-Wallis test?
A) 8.16
B) -8.98
C) 4.94
D) 11.19

Question

A researcher tests three different brands of $2 \%$ milk to see how many grams of fat are in e 8 ounce glass. The results are shown below along with the sums of the ranks of the differ brands.
$\begin{array}{ccc}
\hline \text { Brand A } & \text { Brand B } & \text { Brand C } \
\hline 4.68 & 4.64 & 4.70 \
4.66 & 4.67 & 4.68 \
4.64 & 4.68 & 4.71 \
4.71 & 4.66 & 4.69 \
4.67 & 4.69 & 4.70 \
\hline
\end{array}$

$$\boldsymbol { R } _ { \mathbf { A } } = 33 ; \boldsymbol { R } _ { \mathbf { B } } = 29 ; \boldsymbol { R } _ { \mathbf { C } } = 58$$ What is the test value for the Kruskal-Wallis test?
A) 8.16
B) -8.98
C) 4.94
D) 11.19

Quizplus · Accepted Answer

The Kruskal-Wallis test value is calculated using the formula: $$H = \frac{12}{N(N+1)}\sum_{i=1}^{k}\frac{R_i^2}{n_i} - 3(N+1)$$ where $N$ is the total number of observations, $k$ is the number of groups, $R_i$ is the sum of ranks for group $i$, and $n_i$ is the number of observations in group $i$. Given $R_A = 33$, $R_B = 29$, $R_C = 58$, and each group having 5 observations ($n_i = 5$ for all $i$), and $N = 15$, substituting these values into the formula gives a test value of 4.94.

A Researcher Tests Three Different Brands Of 2%2 \%2% Milk to See How Many Grams of Fat Are in to See

A Researcher Tests Three Different Brands Of $2 \%$ Milk to See How Many Grams of Fat Are in to See