S4 June 2008 Q7
7. An engineering firm buys steel rods. The steel rods from its present supplier are known to have a mean tensile strength of 230 N/mm2.
A new supplier of steel rods offers to supply rods at a cheaper price than the present supplier. A random sample of ten rods from this new supplier gave tensile strengths, \(x\) N/mm2, which are summarised below.
| Sample size | \(\Sigma x\) | \(\Sigma x^2\) |
|---|---|---|
| 10 | 2283 | 524 079 |
(a) Stating your hypotheses clearly, and using a 5% level of significance, test whether or not the rods from the new supplier have a tensile strength lower than the present supplier. (You may assume that the tensile strength is normally distributed). (7)
(b) In the light of your conclusion to part (a) write down what you would recommend the engineering firm to do. (1)
| Scheme | Marks |
|---|---|
| \(\mathrm{H}_0 : \mu = 230 \quad \mathrm{H}_1 : \mu \lt 230\) | B1 |
| \(\nu = 9\) From table critical value \(= \pm 1.833\) | B1ft |
| \(\bar{x} = 228.3 \quad S = 17.858\) | B1 B1 |
| \(t = \dfrac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}\) | M1 |
| \(= \pm\dfrac{228.3 - 230}{\frac{17.858}{\sqrt{10}}} = \pm 0.301\) | A1 |
| \(\pm 0.301 \gt \pm 1.833\). No evidence to reject \(\mathrm{H}_0\). Mean is 230 N/mm2 | B1 |
| (7) |
| Scheme | Marks |
|---|---|
| Since the tensile strength is the same and the price is cheaper recommend use new supplier. | B1 |
| (1) |