| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | CI from raw data list |
| Difficulty | Standard +0.3 This is a straightforward small-sample confidence interval question using the t-distribution. Students must calculate sample mean and standard deviation from given summations, find the appropriate t-critical value, construct the interval, state the normality assumption, and make a simple comparison to £650. All steps are routine S4 procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 5.05d Confidence intervals: using normal distribution |
A town council is concerned that the mean price of renting two bedroom flats in the town has exceeded £650 per month. A random sample of eight two bedroom flats gave the following results, £$x$, per month.
705, 640, 560, 680, 800, 620, 580, 760
[You may assume $\sum x = 5345$ and $\sum x^2 = 3621025$]
\begin{enumerate}[label=(\alph*)]
\item Find a 90\% confidence interval for the mean price of renting a two bedroom flat.
[6]
\item State an assumption that is required for the validity of your interval in part (a).
[1]
\item Comment on whether or not the town council is justified in being concerned. Give a reason for your answer.
[2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 Q4 [9]}}