| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Wilcoxon tests |
| Type | Paired t-test |
| Difficulty | Standard +0.3 This is a straightforward paired t-test application 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 (8 marks), it's a routine textbook exercise with no conceptual challenges beyond applying the standard paired t-test algorithm, making it slightly easier than average. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
| Rope no. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| Dry rope | 9.7 | 8.5 | 6.3 | 8.3 | 7.2 | 5.4 | 6.8 | 8.1 | 5.9 |
| Wet rope | 9.1 | 9.5 | 8.2 | 9.7 | 8.5 | 4.9 | 8.4 | 8.7 | 7.7 |
2. An engineer decided to investigate whether or not the strength of rope was affected by water. A random sample of 9 pieces of rope was taken and each piece was cut in half. One half of each piece was soaked in water over night, and then each piece of rope was tested to find its strength. The results, in coded units, are given in the table below
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | c | }
\hline
Rope no. & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
\hline
Dry rope & 9.7 & 8.5 & 6.3 & 8.3 & 7.2 & 5.4 & 6.8 & 8.1 & 5.9 \\
\hline
Wet rope & 9.1 & 9.5 & 8.2 & 9.7 & 8.5 & 4.9 & 8.4 & 8.7 & 7.7 \\
\hline
\end{tabular}
\end{center}
Assuming that the strength of rope follows a normal distribution, test whether or not there is any difference between the mean strengths of dry and wet rope. State your hypotheses clearly and use a $1 \%$ level of significance.\\
(8 marks)\\
\hfill \mbox{\textit{Edexcel S4 Q2 [8]}}