| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | T-tests (unknown variance) |
| Type | Single sample t-test |
| Difficulty | Standard +0.3 This is a straightforward one-sample t-test with clearly stated hypotheses, standard calculations from summary statistics (mean, variance, test statistic), and comparison to critical value. The context is applied but the statistical procedure is routine for S4, requiring only systematic application of a standard technique with no novel insight or complex reasoning. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
| Sample size | \(\Sigma x\) | \(\Sigma x^2\) |
| 10 | 2283 | 524079 |
An engineering firm buys steel rods. The steel rods from its present supplier are known to have a mean tensile strength of 230 N/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, $x$ N/mm$^2$, which are summarised below.
\begin{tabular}{|c|c|c|}
\hline
Sample size & $\Sigma x$ & $\Sigma x^2$ \\
\hline
10 & 2283 & 524079 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\alph*)]
\item 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]
\item In the light of your conclusion to part (a) write down what you would recommend the engineering firm to do.
[1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 Q7 [8]}}