| Exam Board | OCR |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2009 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | T-tests (unknown variance) |
| Type | Confidence interval derived quantity |
| Difficulty | Standard +0.3 This is a straightforward application of t-distribution confidence intervals with small sample size. Part (i) requires standard calculation of sample mean, sample standard deviation, and applying the t-interval formula. Part (ii) is a simple linear transformation (multiply by 2π). The question is slightly above average difficulty only because it involves the t-distribution rather than z, but follows a completely standard procedure with no conceptual challenges. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean5.05d Confidence intervals: using normal distribution |
3 A machine produces circular metal discs whose radii have a normal distribution with mean $\mu \mathrm { cm }$. A random sample of five discs is selected and their radii, in cm, are as follows.
$$\begin{array} { l l l l l }
6.47 & 6.52 & 6.46 & 6.47 & 6.51
\end{array}$$
(i) Calculate a $95 \%$ confidence interval for $\mu$.\\
(ii) Hence state a 95\% confidence interval for the mean circumference of a disc.
\hfill \mbox{\textit{OCR S3 2009 Q3 [7]}}