jack89515lg

2021-11-26

You measure the length of copperheads in cm. You want to know if there is a difference in length between male and female copperheads. You get the following results, but discover the data are NOT normally distributed.
$\begin{array}{|c|}\hline Sex\\ males:& 64& 72& 73& 74& 76& 76& 77& 114& 78.25& 15.01\\ females:& 31& 54& 55& 56& 57& 58& 65& 67& 55.38& 10.91\\ \hline\end{array}$
Give the value of the test statistic (e.g., U* or t*, whichever is correct) for these data.

Alicia Washington

Step 1
Define the hypotheses:
Null hypothesis $\left({H}_{0}\right)$:
${H}_{0}$: There is no significant difference in the lengths of male and female copperheads.
Alternative hypothesis $\left({H}_{1}\right)$:
${H}_{1}$: There is a significant difference in the lengths of male and female copperheads.
This is a two-tailed test of significance.
Step 2
Ranking:
The ra
are obtained as given below:

Test statistic calculation:
Here, ${R}_{1}=144,{R}_{2}=66$.
${U}_{1}={n}_{1}{n}_{2}+\frac{{n}_{1}\left({n}_{1}+1\right)}{2}-{R}_{1}$
$=\left(10×10\right)+\frac{10×11}{2}-144$
$=100+55-144$
$=11$
${U}_{2}={n}_{1}{n}_{2}+\frac{{n}_{2}\left({n}_{2}+1\right)}{2}-{R}_{2}$
$=\left(10×10\right)+\frac{10×11}{2}-66$
$=100+55-66$
$=89$
$U=min\left\{{U}_{1},{U}_{2}\right\}$
$=min\left\{11,89\right\}$
$=11$.
Thus, the test statistic is 11.

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