| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | CI from raw data list |
| Difficulty | Challenging +1.3 This S4 question requires confidence intervals for variance using chi-squared distribution and an F-test for comparing two variances. While these are advanced statistical topics beyond basic A-level, they follow standard procedures taught in S4. Part (a) involves calculating sample variance and applying chi-squared critical values (7 marks suggests multiple steps but routine application). Part (b) requires an F-test with clear hypothesis setup. The calculations are methodical rather than requiring novel insight, though the topics themselves are specialist and the chi-squared/F-distribution tables must be used correctly. |
| Spec | 5.05d Confidence intervals: using normal distribution |
The weights, in grams, of apples are assumed to follow a normal distribution.
The weights of apples sold by a supermarket have variance $\sigma_1^2$. A random sample of 4 apples from the supermarket had weights
114, 100, 119, 123.
\begin{enumerate}[label=(\alph*)]
\item Find a 95\% confidence interval for $\sigma_1^2$. [7]
\end{enumerate}
The weights of apples sold on a market stall have variance $\sigma_M^2$. A second random sample of 7 apples was taken from the market stall. The sample variance $s_M^2$ of the apples was 318.8.
\begin{enumerate}[label=(\alph*)]
\item[(b)] Stating your hypotheses clearly test, at the 1\% level of significance, whether or not there is evidence that $\sigma_M^2 > \sigma_1^2$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 Q2 [12]}}