| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | T-tests (unknown variance) |
| Type | Paired sample t-test |
| Difficulty | Standard +0.3 This is a standard paired t-test question requiring calculation of differences, sample statistics, and hypothesis testing with a specified value. While it involves multiple steps (computing differences, finding mean/SD, calculating test statistic, comparing to critical value), it follows a routine S4 procedure with no conceptual challenges or novel insights required. Slightly easier than average due to its straightforward paired design and clear structure. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
| Person | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Heart rate lying down | 66 | 70 | 59 | 65 | 72 | 66 | 62 | 69 | 56 | 68 |
| Heart rate standing up | 75 | 76 | 63 | 67 | 80 | 75 | 65 | 74 | 63 | 75 |
As part of an investigation, a random sample of 10 people had their heart rate, in beats per minute, measured whilst standing up and whilst lying down. The results are summarised below.
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
Person & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
\hline
Heart rate lying down & 66 & 70 & 59 & 65 & 72 & 66 & 62 & 69 & 56 & 68 \\
\hline
Heart rate standing up & 75 & 76 & 63 & 67 & 80 & 75 & 65 & 74 & 63 & 75 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\alph*)]
\item State one assumption that needs to be made in order to carry out a paired $t$-test.
[1]
\item Test, at the 5\% level of significance, whether or not there is any evidence that standing up increases people's mean heart rate by more than 5 beats per minute. State your hypotheses clearly.
[8]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 Q2 [9]}}