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      <text>43.2.05 Pearson signif eg</text>
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      <text><![CDATA[<h4 class="HELM_example">Example</h4>
<p>Test the significance of the value of \(r\) obtained from the previous example concerning electric
motor torque values. Use the \(5\%\) level of  significance. 
</p><h4 class="HELM_solution">Solution</h4>
<p></p>
The sample size is \(7\) so we have \(5\) degrees of freedom. The value of \(r_{test}\) is given by
\[ r_{test} = \dfrac{r \sqrt{n-2}}{\sqrt{1-r^2}} = \dfrac{0.46 \times \sqrt{7-2}}{\sqrt{1 - 0.46^2}} = 1.158. \]<p></p>
From Table 2, the critical value for a two-sided test at the \(5\%\) level of  significance is \(2.571\). In
this case, since \(1.158 &lt; 2.571\) we cannot reject the null hypothesis at the \(5\%\) level of significance and conclude that for the motor under investigation, there is no evidence of a relationship between torque produced and current used.]]></text>
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