| Exam Board | WJEC |
|---|---|
| Module | Unit 4 (Unit 4) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Pearson’s product-moment correlation coefficient |
| Type | Two-tailed test for any correlation |
| Difficulty | Moderate -0.3 This is a straightforward application of hypothesis testing for correlation with standard procedures: stating H₀ and H₁, comparing r=0.895 to critical values from tables for n=17, and interpreting a given p-value. Part (a) requires only routine recall of the test procedure with no problem-solving, while part (b) is even simpler—just interpreting a p-value. The question is slightly easier than average because it's highly structured and requires no derivation or insight, though it does involve multiple parts and contextual interpretation. |
| Spec | 2.02c Scatter diagrams and regression lines2.02d Informal interpretation of correlation2.05f Pearson correlation coefficient2.05g Hypothesis test using Pearson's r5.08a Pearson correlation: calculate pmcc5.08d Hypothesis test: Pearson correlation |
| Value for money | Cost per night | |||
| Value for money | 1 | |||
| Cost per night |
| 1 |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(H_0: \rho = 0\) | B1 | AO3 |
| \(H_1: \rho \neq 0 \text{ two-sided}\) | — | — |
| \(TS = 0.895\) | B1 | AO1 |
| \(CV = \pm 0.4821\) | B1 | AO1 |
| \(\text{Since } TS > 0.4821, \text{ Reject } H_0\) | B1 | AO2 |
| \(\text{Strong evidence to suggest the correlation coefficient is greater than zero}\) | E1 | AO3 |
| (b) \(p\text{-value for correlation between Value for money and Cost per night is } > 0.05\) | E1 | AO2 |
| \(\text{Cost per night does not seem to be correlated to Value for money.}\) | E1 | AO2 |
**(a)** $H_0: \rho = 0$ | B1 | AO3 | $H_0: \rho = 0$; $H_1: \rho > 0$ one-sided; Population stated or implied |
| $H_1: \rho \neq 0 \text{ two-sided}$ | — | — | |
| $TS = 0.895$ | B1 | AO1 | $TS = 0.895$ |
| $CV = \pm 0.4821$ | B1 | AO1 | $CV = \pm 0.412$ |
| $\text{Since } TS > 0.4821, \text{ Reject } H_0$ | B1 | AO2 | Since $TS > 0.412$, Reject $H_0$ |
| $\text{Strong evidence to suggest the correlation coefficient is greater than zero}$ | E1 | AO3 | Strong evidence to suggest the correlation coefficient is greater than zero |
**(b)** $p\text{-value for correlation between Value for money and Cost per night is } > 0.05$ | E1 | AO2 | |
| $\text{Cost per night does not seem to be correlated to Value for money.}$ | E1 | AO2 | |5. A hotel owner in Cardiff is interested in what factors hotel guests think are important when staying at a hotel. From a hotel booking website he collects the ratings for 'Cleanliness', 'Location', 'Comfort' and 'Value for money' for a random sample of 17 Cardiff hotels.\\
(Each rating is the average of all scores awarded by guests who have contributed reviews using a scale from 1 to 10 , where 10 is 'Excellent'.)
The scatter graph shows the relationship between 'Value for money' and 'Cleanliness' for the sample of Cardiff hotels.\\
\includegraphics[max width=\textwidth, alt={}, center]{b35e94ab-a426-4fca-9ecb-c659e0143ed7-4_693_1033_749_516}
\begin{enumerate}[label=(\alph*)]
\item The product moment correlation coefficient for 'Value for money' and 'Cleanliness' for the sample of 17 Cardiff hotels is 0.895 . Stating your hypotheses clearly, test, at the $5 \%$ level of significance, whether this correlation is significant. State your conclusion in context.
\item The hotel owner also wishes to investigate whether 'Value for money' has a significant correlation with 'Cost per night'. He used a statistical analysis package which provided the following output which includes the Pearson correlation coefficient of interest and the corresponding $p$-value.
\begin{center}
\begin{tabular}{ | c | c | c | }
\hline
& Value for money & Cost per night \\
\hline
Value for money & 1 & \\
\hline
Cost per night & \begin{tabular}{ c }
0.047 \\
$( 0.859 )$ \\
\end{tabular} & 1 \\
\hline
\end{tabular}
\end{center}
Comment on the correlation between 'Value for money' and 'Cost per night'.
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 4 Q5 [7]}}