| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2020 |
| Session | May |
| Marks | 10 |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Hypothesis test for association |
| Difficulty | Standard +0.3 This is a straightforward application of Spearman's rank correlation coefficient with standard hypothesis testing. Students must rank data, apply the formula (or use given ranks), and compare to critical values. The ranking is mechanical, the hypothesis test is routine, and part (iii) requires standard recall about when PMCC vs Spearman's is appropriate. Slightly above average difficulty only due to the data handling and multiple parts, but no novel insight required. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Runner | A | B | C | D | E | F | G | H | I |
| 100 metre time (seconds) | 13.2 | 11.6 | 10.9 | 12.3 | 14.7 | 13.1 | 11.7 | 13.6 | 12.4 |
| Push-ups achieved | 32 | 42 | 22 | 36 | 41 | 27 | 37 | 38 | 33 |
14.
Nine long-distance runners are starting an exercise programme to improve their strength. During the first session, each of them has to do a 100 metre run and to do as many push-ups as possible in one minute. The times taken for the run, together with the number of push-ups each runner achieves, are shown in the table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | c | }
\hline
Runner & A & B & C & D & E & F & G & H & I \\
\hline
100 metre time (seconds) & 13.2 & 11.6 & 10.9 & 12.3 & 14.7 & 13.1 & 11.7 & 13.6 & 12.4 \\
\hline
Push-ups achieved & 32 & 42 & 22 & 36 & 41 & 27 & 37 & 38 & 33 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\roman*)]
\item Calculate the value of Spearman's rank correlation coefficient.
\item Carry out a hypothesis test at the $5 \%$ significance level to examine whether there is any association between time taken for the run and number of push-ups achieved. [4]
\item Under what circumstances is it appropriate to carry out a hypothesis test based on the product moment correlation coefficient. State, with a reason, which test is more appropriate for these data.
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2020 Q14 [10]}}