| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | CI from raw data list |
| Difficulty | Standard +0.3 This is a straightforward S4 confidence interval question requiring standard calculations for mean (using t-distribution) and variance (using chi-squared distribution) from given data, followed by basic interpretation. While it involves multiple distributions and careful calculation, it follows textbook procedures with no novel problem-solving or conceptual challenges beyond routine application of formulas. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean5.05d Confidence intervals: using normal distribution |
A supervisor wishes to check the typing speed of a new typist. On 10 randomly selected occasions, the supervisor records the time taken for the new typist to type 100 words. The results, in seconds, are given below.
110, 125, 130, 126, 128, 127, 118, 120, 122, 125
The supervisor assumes that the time taken to type 100 words is normally distributed.
\begin{enumerate}[label=(\alph*)]
\item Calculate a 95\% confidence interval for
\begin{enumerate}[label=(\roman*)]
\item the mean,
\item the variance
\end{enumerate}
of the population of times taken by this typist to type 100 words. [13]
\end{enumerate}
The supervisor requires the average time needed to type 100 words to be no more than 130 seconds and the standard deviation to be no more than 4 seconds.
\begin{enumerate}[label=(\alph*)]
\item[(b)] Comment on whether or not the supervisor should be concerned about the speed of the new typist. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 Q6 [16]}}