A technician is interested in comparing the time it takes to assemble a certain computer component using three different machines. Workers are randomly selected and randomly assigned to one of the machines. The assembly times (in minutes) are shown in the table.
Use the Kruskal-Wallis H-test to test whether the distributions of assembly times differ for the three different machines. Be sure to specify the null and alternative hypotheses. Use $\alpha = 0.05$ $$\begin{array} { c | c | c }
\text { Machine 1 } & \text { Machine 2 } & \text { Machine 3 } \
\hline 38 & 46 & 34 \
37 & 35 & 31 \
38 & 44 & 35 \
36 & 39 & 37 \
39 & 41 & 36 \
37 & 38 & 33 \
38 & 42 & 43
\end{array}$$

Question

A technician is interested in comparing the time it takes to assemble a certain computer component using three different machines. Workers are randomly selected and randomly assigned to one of the machines. The assembly times (in minutes) are shown in the table.
Use the Kruskal-Wallis H-test to test whether the distributions of assembly times differ for the three different machines. Be sure to specify the null and alternative hypotheses. Use $\alpha = 0.05$ $$\begin{array} { c | c | c } 
\text { Machine 1 } & \text { Machine 2 } & \text { Machine 3 } \
\hline 38 & 46 & 34 \
37 & 35 & 31 \
38 & 44 & 35 \
36 & 39 & 37 \
39 & 41 & 36 \
37 & 38 & 33 \
38 & 42 & 43
\end{array}$$

Quizplus · Accepted Answer

The Answer is

\mathrm { H } _ { 0 }

: The distributions of assembly times are the same for the three different machines

\mathrm { H } _ { \mathrm { a } }

: At least two of the three machines have assembly time distributions that differ in location
Critical value

5.991

; test statistic

\mathrm { H } \approx 7.482

; reject

\mathrm { H } _ { 0 }

There is enough evidence to conclude that at least two of the three machines have assembly time distributions that differ in location.

A Technician Is Interested in Comparing the Time It Takes α=0.05\alpha = 0.05α=0.05

A Technician Is Interested in Comparing the Time It Takes $\alpha = 0.05$