Answer
We accept the claim that taxi-out times for Flight 19 and Flight 21 have the same median.
Work Step by Step
Let the null hypothesis be:
$H_{0}:R_{1}=R_{2} $
(The two populations have equal medians.)
Let the alternative hypothesis be:
$H_{1}:R_{1} \ne R_{2}$
(The two populations don't have equal medians.)
Rank Sum for Flight 19 $= 128$
Rank Sum for Flight 21 $= 172$
$\mu_{R}=150$
$\sigma _{R}=17.3205$
Compute the z-score:
$z=\frac{R-\mu_{R}}{\sigma_{R}}=\frac{128-150}{17.3205}=−1.270$
We are testing (with $α=0.05$) if the hypothesis that the two populations have equal medians is true. So, we have a two-tailed test with critical values $z=±1.96$. The test statistic of $z=−1.270$ does not fall within the critical region, so we fail to reject the null hypothesis that taxi-out times for Flight 19 and Flight 21 have the same median.
