| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | CI from raw data list |
| Difficulty | Challenging +1.2 This is a standard S4 confidence interval question requiring calculation of CI for mean (using t-distribution), CI for variance (using chi-squared distribution), and then applying these to estimate a proportion. While it involves multiple distributions and several steps (16 marks total), these are well-practiced techniques in S4 with no novel problem-solving required. The final part requires some thought about which confidence limits maximize the proportion, elevating it slightly above routine but still within standard S4 territory. |
| Spec | 5.05d Confidence intervals: using normal distribution |
A random sample of 15 strawberries is taken from a large field and the weight $x$ grams of each strawberry is recorded. The results are summarised below.
$$\sum x = 291 \quad \sum x^2 = 5968$$
Assume that the weights of strawberries are normally distributed.
Calculate a 95\% confidence interval for
\begin{enumerate}[label=(\alph*)]
\item (i) the mean of the weights of the strawberries in the field,
(ii) the variance of the weights of the strawberries in the field.
[12]
\end{enumerate}
Strawberries weighing more than 23g are considered to be less tasty.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumii}{1}
\item Use appropriate confidence limits from part (a) to find the highest estimate of the proportion of strawberries that are considered to be less tasty.
[4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 Q4 [16]}}