Answer
There is sufficient evidence to reject the null hypothesis that the median amount of strontium-90 from Pennsylvania residents is the same as the median from New York residents.
Work Step by Step
Let the null hypothesis be
$H_{0}:R1=R2 $
(The two populations have equal medians.)
Let the alternative hypothesis be
$H_{1}:R1≠R2$
(The two populations don't have equal medians.)
Rank Sum for the first sample = $194.5$
$\mu_{R}=150$
$\sigma_{R}=17.32051$
$z=\frac{R-\mu_{R}}{\sigma_{R}}=\frac{194.5-150}{17.32051}=2.57$
We are testing (with $\alpha=0.05$) the hypothesis that the two populations have equal medians, so we have a two-tailed test with critical values $z=\pm1.96$. The test statistic falls in the critical region bounded by the critical values of $-1.96$ and $1.96$, so we can reject the null hypothesis that the median amount of strontium-90 from Pennsylvania residents is the same as the median amount from New York residents.
