| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | F-test and chi-squared for variance |
| Type | Chi-squared test then t-test sequential |
| Difficulty | Standard +0.3 This is a standard two-part hypothesis testing question requiring chi-squared test for variance and t-test for mean. While it involves S4 content (hypothesis testing with normal distributions), both parts follow routine procedures with clear hypotheses, standard test statistics, and straightforward conclusions. The calculations are mechanical with no conceptual challenges beyond applying learned formulas. |
| Spec | 5.05d Confidence intervals: using normal distribution |
The length $X$ mm of a spring made by a machine is normally distributed N($\mu, \sigma^2$). A random sample of 20 springs is selected and their lengths measured in mm. Using this sample the unbiased estimates of $\mu$ and $\sigma^2$ are
$\bar{x} = 100.6$, $s^2 = 1.5$.
Stating your hypotheses clearly test, at the 10\% level of significance,
\begin{enumerate}[label=(\alph*)]
\item whether or not the variance of the lengths of springs is different from 0.9, [6]
\item whether or not the mean length of the springs is greater than 100 mm. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 Q4 [12]}}