| Exam Board | SPS |
|---|---|
| Module | SPS ASFM Statistics (SPS ASFM Statistics) |
| Year | 2021 |
| Session | May |
| Marks | 8 |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Hypothesis test for association |
| Difficulty | Moderate -0.3 This is a straightforward Spearman's rank correlation question testing standard procedures: recognizing impossible values (part i requires knowing the formula bounds), algebraic rearrangement to find Σd² (part ii), and executing a routine hypothesis test (part iii). All parts follow textbook methods with no novel insight required, making it slightly easier than average despite being multi-part. |
| Spec | 2.05a Hypothesis testing language: null, alternative, p-value, significance2.05c Significance levels: one-tail and two-tail5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
Arlosh, Sarah and Desi are investigating the ratings given to six different films by two critics.
\begin{enumerate}[label=(\roman*)]
\item Arlosh calculates Spearman's rank correlation coefficient $r_s$ for the critics' ratings. He calculates that $\Sigma d^2 = 72$. Show that this value must be incorrect. [2]
\item Arlosh checks his working with Sarah, whose answer $r_s = \frac{39}{35}$ is correct. Find the correct value of $\Sigma d^2$. [2]
\item Carry out an appropriate two-tailed significance test of the value of $r_s$ at the 5% significance level, stating your hypotheses clearly. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS ASFM Statistics 2021 Q5 [8]}}