7. What are the advantages and drawbacks of non parametric methods over parametric methods? Describe the procedure of median test to test the hypothesis. What non parametric test would you use when two samples are related?
A certain type of light bulb produced by two different manufacturers, \( X \) and \( Y \), by testing 10 bulbs selected at random from each of the outputs. The data, in hundreds of hours used before failure are as follows:
\[
\begin{array}{l}
x: 5.64 .66 .84 .96 .15 .34 .55 .85 .44 .7 \\
y: 7.28 .15 .17 .36 .97 .85 .96 .76 .57 .1
\end{array}
\]
Use the Wilcoxon test to test the equality of medians of the failure times at the approximate \( 5 \% \) significance level.
