| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2008 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Z-tests (known variance) |
| Type | One-tail z-test (lower tail) |
| Difficulty | Standard +0.3 This is a straightforward one-tail z-test with clearly stated hypotheses, given summary statistics, and standard interpretation. While it's Further Maths (S4), the mechanics are routine: calculate sample mean, perform z-test using assumed known variance from sample, compare to critical value, and make a contextual recommendation. Slightly above average difficulty due to being FM content, but the execution is entirely procedural with no conceptual challenges. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
| Sample size | \(\Sigma x\) | \(\Sigma x ^ { 2 }\) |
| 10 | 2283 | 524079 |
\begin{enumerate}
\item An engineering firm buys steel rods. The steel rods from its present supplier are known to have a mean tensile strength of $230 \mathrm {~N} / \mathrm { mm } ^ { 2 }$.
\end{enumerate}
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.
\begin{center}
\begin{tabular}{ | c | c | c | }
\hline
Sample size & $\Sigma x$ & $\Sigma x ^ { 2 }$ \\
\hline
10 & 2283 & 524079 \\
\hline
\end{tabular}
\end{center}
(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 that the present supplier. (You may assume that the tensile strength is normally distributed).\\
(b) In the light of your conclusion to part (a) write down what you would recommend the engineering firm to do.
\hfill \mbox{\textit{Edexcel S4 2008 Q7 [8]}}