| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2009 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | Find minimum sample size |
| Difficulty | Standard +0.3 Part (a) is straightforward calculation of sample mean and unbiased variance using standard formulas. Part (b) requires applying the confidence interval formula and rearranging to find n, which is a standard S3 technique but involves slightly more steps than routine questions. Overall slightly easier than average due to direct application of learned procedures. |
| Spec | 5.05b Unbiased estimates: of population mean and variance5.05c Hypothesis test: normal distribution for population mean |
A company produces climbing ropes. The lengths of the climbing ropes are normally distributed. A random sample of 5 ropes is taken and the length, in metres, of each rope is measured. The results are given below.
120.3 \quad 120.1 \quad 120.4 \quad 120.2 \quad 119.9
\begin{enumerate}[label=(\alph*)]
\item Calculate unbiased estimates for the mean and the variance of the lengths of the climbing ropes produced by the company. [5]
\end{enumerate}
The lengths of climbing rope are known to have a standard deviation of 0.2 m. The company wants to make sure that there is a probability of at least 0.90 that the estimate of the population mean, based on a random sample size of $n$, lies within 0.05 m of its true value.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the minimum sample size required. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2009 Q7 [11]}}