| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2007 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Wilcoxon tests |
| Type | Paired t-test |
| Difficulty | Standard +0.3 This is a straightforward application of a paired t-test with clear data and standard procedure. Students must calculate differences, find mean and standard deviation, compute the test statistic, and compare to critical values. While it requires multiple computational steps, it's a routine textbook exercise with no conceptual challenges beyond knowing the standard paired t-test procedure. |
| Spec | 5.05d Confidence intervals: using normal distribution |
| Person | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) | \(I\) | \(J\) |
| Arm cuff | 140 | 110 | 138 | 127 | 142 | 112 | 122 | 128 | 132 | 160 |
| Finger monitor | 154 | 112 | 156 | 152 | 142 | 104 | 126 | 132 | 144 | 180 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\bar{d} = \pm 9.1\) | M1 | |
| \((\sum d = 91, \sum x^2 = 1789)\) | ||
| \(sd = \sqrt{106.7} = 10.332...\) | A1 A1 | |
| \(H_0 : \mu_d = 0\) | ||
| \(H_1 : \mu_d \neq 0\) | B1 | |
| \(t = \pm \frac{9.1\sqrt{10}}{10.332} = \pm 2.785\) | M1 A1 | |
| Critical value \(t_9 = \pm 1.833\) | B1 | |
| Significant. There is a difference between blood pressure measured by arm cuff and finger monitor. | A1 | |
| awrt \(\pm 2.78\) or \(2.79\) | Total: 8 marks |
| Answer | Marks |
|---|---|
| The difference in measurements of blood pressure is normally distributed | B1 |
Total: 1 mark
**Part a:**
Data: $d: 14, 2, 18, 25, 0, -8, 4, 4, 12, 20$
$\bar{d} = \pm 9.1$ | M1 |
$(\sum d = 91, \sum x^2 = 1789)$ | |
$sd = \sqrt{106.7} = 10.332...$ | A1 A1 |
$H_0 : \mu_d = 0$ | |
$H_1 : \mu_d \neq 0$ | B1 |
$t = \pm \frac{9.1\sqrt{10}}{10.332} = \pm 2.785$ | M1 A1 |
Critical value $t_9 = \pm 1.833$ | B1 |
Significant. There is a difference between blood pressure measured by arm cuff and finger monitor. | A1 |
**awrt** $\pm 2.78$ or $2.79$ | | Total: 8 marks
**Part b:**
The difference in measurements of blood pressure is normally distributed | B1 |
Notes:
- (a) One tail test: Loses the first B1. CV is 1.383 in this case. Can get 7/8
- (b) Looking for the difference in measurements. Not just that it is normally distributed.
Total: 1 mark
---\begin{enumerate}
\item A medical student is investigating two methods of taking a person's blood pressure. He takes a random sample of 10 people and measures their blood pressure using an arm cuff and a finger monitor. The table below shows the blood pressure for each person, measured by each method.
\end{enumerate}
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | c | c | }
\hline
Person & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ & $H$ & $I$ & $J$ \\
\hline
Arm cuff & 140 & 110 & 138 & 127 & 142 & 112 & 122 & 128 & 132 & 160 \\
\hline
Finger monitor & 154 & 112 & 156 & 152 & 142 & 104 & 126 & 132 & 144 & 180 \\
\hline
\end{tabular}
\end{center}
(a) Use a paired $t$-test to determine, at the $10 \%$ level of significance, whether or not there is a difference in the mean blood pressure measured using the two methods. State your hypotheses clearly.\\
(8)\\
(b) State an assumption about the underlying distribution of measured blood pressure required for this test.\\
(1)\\
\hfill \mbox{\textit{Edexcel S4 2007 Q1 [9]}}