Chapter 14.2, Problem 3Q

Below are $n=50$ computer-generated observations that are presumably a random sample from the exponential pdf, $f_Y\left(y\right)=e^{-y},y\ge 0.$ Use Theorem 14.2.1 to test whether the difference between the sample median for these $y_i\text{'}s\left(=0.604\right)$ and the true median of $f_Y\left(y\right)$ is statistically significant. Let $a=\mathrm{0.05.}$

$\begin{array}{l}\text{0}\text{.27187 0}\text{.46495 0}\text{.19368 0}\text{.80433 1}\text{.25450 0}\text{.62962 1}\text{.88300 }\\ \text{1}\text{.31951 2}\text{.53918 1}\text{.21187 0}\text{.95834 0}\text{.49017 0}\text{.87230 0}\text{.88571 }\\ \text{1}\text{.41717 1}\text{.75994 0}\text{.60280 2}\text{.19654 0}\text{.00594 4}\text{.11127 0}\text{.24130 }\\ \text{0}\text{.16473 0}\text{.08178 1}\text{.01424 0}\text{.60511 0}\text{.87973 0}\text{.06127 0}\text{.24758 }\\ \text{0}\text{.54407 0}\text{.05267 0}\text{.75210 0}\text{.13538 0}\text{.42956 0}\text{.02261 1}\text{.20378 }\\ \text{1}\text{.09271 1}\text{.88705 0}\text{.17500 0}\text{.50194 0}\text{.52122 0}\text{.02915 0}\text{.27348 }\\ \text{0}\text{.08916 0}\text{.72997 0}\text{.37185 0}\text{.06500 1}\text{.47721 4}\text{.02733 0}\text{.64003 }\\ \text{0}\text{.05603}\end{array}$