| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2013 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Central limit theorem |
| Type | Unbiased estimator from raw data |
| Difficulty | Moderate -0.5 This is a straightforward application of standard formulas for unbiased estimators and confidence intervals. Part (a) requires routine calculation of sample mean and variance using n-1 denominator, part (b) involves combining samples using weighted means (a slightly less routine step), and part (c) is a standard confidence interval calculation. While multi-part and requiring careful arithmetic, it demands no problem-solving insight beyond direct formula application. |
| Spec | 5.05b Unbiased estimates: of population mean and variance5.05d Confidence intervals: using normal distribution |
\begin{enumerate}
\item Lambs are born in a shed on Mill Farm. The birth weights, $x \mathrm {~kg}$, of a random sample of 8 newborn lambs are given below.
\end{enumerate}
$$\begin{array} { l l l l l l l l }
4.12 & 5.12 & 4.84 & 4.65 & 3.55 & 3.65 & 3.96 & 3.40
\end{array}$$
(a) Calculate unbiased estimates of the mean and variance of the birth weight of lambs born on Mill Farm.
A further random sample of 32 lambs is chosen and the unbiased estimates of the mean and variance of the birth weight of lambs from this sample are 4.55 and 0.25 respectively.\\
(b) Treating the combined sample of 40 lambs as a single sample, estimate the standard error of the mean.
The owner of Mill Farm researches the breed of lamb and discovers that the population of birth weights is normally distributed with standard deviation 0.67 kg .\\
(c) Calculate a $95 \%$ confidence interval for the mean birth weight of this breed of lamb using your combined sample mean.
\hfill \mbox{\textit{Edexcel S3 2013 Q7 [13]}}