Question: "The number of points held by a sample..."

tapetivk

Answered question

2021-12-04

The number of points held by a sample of the NHLs

Answer & Explanation

William Yazzie

Beginner2021-12-05Added 20 answers

$\begin{array}{cc} Eastern Conference (X) & Western Conference(Y) & (x - x b a r)^{2} & (y - y b a r)^{2} \\ 83 & 77 & 211.5702 & 281.4938 \\ 60 & 59 & 71.479 & 1.493827 \\ 75 & 72 & 42.84298 & 138.716 \\ 68 & 58 & 0.206612 & 4.938272 \\ 78 & 37 & 91.1157 & 539.2716 \\ 69 & 57 & 0.297521 & 10.38272 \\ 70 & 66 & 2.38843 & 33.38272 \\ 68 & 55 & 0.206612 & 27.2716 \\ 62 & 61 & 41.66116 & 0.604938 \\ 61 & 55.57025 \\ 59 & 89.38843 \end{array}$
$\overset{―}{x} = \frac{1}{n} \sum x$
- Eastern
$\overset{―}{x} = \frac{753}{11} = 68.4545$
- Western
$\overset{―}{y} = \frac{542}{9} = 60.222$
$s = \sqrt{\frac{1}{n - 1} \sum {(x - \overset{―}{x})}^{2}}$
- Eastern
$s_{x} = \sqrt{\frac{606.727}{10}} = 7.78927$
- Western
$s_{y} = \sqrt{\frac{1037.556}{8}} = 11.3883$
$H_{0} : u_{E} = u_{W}$
$H_{1} : u_{E} > u_{W}$
$t = \frac{\overset{―}{x} - \overset{―}{y}}{\sqrt{\frac{s_{1}^{2}}{n_{1}} + \frac{s_{2}^{2}}{n_{2}}}}$
$t = \frac{68.4545 - 60.2222}{\sqrt{\frac{{(7.78927)}^{2}}{11} + \frac{{(11.3883)}^{2}}{9}}}$
$t = 1.8442$
p-value $= 0.0408$
Excel formula used: "=T.DIST.RT(G5,18)"
Because the p-value is larger than 0.01, we are unable to rule out the null hypothesis and come to the conclusion that there is inadequate proof that the eastern conference's mean score is higher than the western conference's.

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