| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | Calculate CI from summary stats |
| Difficulty | Standard +0.8 This S4 question requires constructing confidence intervals for both mean (using t-distribution) and variance (using chi-squared distribution), then applying these to estimate a proportion via normal distribution. While each component is standard for S4, part (c) requires synthesizing results and understanding how to use confidence limits to find a 'worst-case' proportion, which demands statistical maturity beyond routine application of formulas. |
| Spec | 5.05d Confidence intervals: using normal distribution |
A machine fills jars with jam. The weight of jam in each jar is normally distributed. To check the machine is working properly the contents of a random sample of 15 jars are weighed in grams. Unbiased estimates of the mean and variance are obtained as
$$\mu = 560 \quad s^2 = 25.2$$
Calculate a 95\% confidence interval for,
\begin{enumerate}[label=(\alph*)]
\item the mean weight of jam,
[4]
\item the variance of the weight of jam.
[5]
\end{enumerate}
A weight of more than 565g is regarded as too high and suggests the machine is not working properly.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumii}{2}
\item Use appropriate confidence limits from parts (a) and (b) to find the highest estimate of the proportion of jars that weigh too much.
[5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 Q5 [14]}}