- An engineering firm buys steel rods. The steel rods from its present supplier are known to have a mean tensile strength of \(230 \mathrm {~N} / \mathrm { mm } ^ { 2 }\).
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, \(x \mathrm { N } / \mathrm { mm } ^ { 2 }\), which are summarised below.
| Sample size | \(\Sigma x\) | \(\Sigma x ^ { 2 }\) |
| 10 | 2283 | 524079 |
- 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 that the present supplier. (You may assume that the tensile strength is normally distributed).
- In the light of your conclusion to part (a) write down what you would recommend the engineering firm to do.