9231 P42 - Nov 2025 - Q5 - 9 marks
6619
An engineer is comparing the tensile strengths of steel rods made from two machines, \(A\) and \(B\). The engineer randomly selects 8 rods from machine \(A\) and 6 rods from machine \(B\). The tensile strengths, in appropriate units, are given in the following table.
| Machine \(A\) | \(402\) | \(403\) | \(415\) | \(412\) | \(409\) | \(407\) | \(406\) | \(410\) |
|---|---|---|---|---|---|---|---|---|
| Machine \(B\) | \(401\) | \(398\) | \(395\) | \(397\) | \(410\) | \(405\) |
You should assume that the two distributions are normal and have the same population variance. Use a \(t\)-test at the \(5\%\) significance level to test whether there is any difference in the mean tensile strengths of steel rods from the two machines.
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