| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2018 |
| Session | December |
| Marks | 6 |
| Topic | Hypothesis test of Pearson’s product-moment correlation coefficient |
| Type | Justify one-tailed vs two-tailed choice |
| Difficulty | Moderate -0.8 This is a straightforward hypothesis testing question requiring standard recall of correlation testing procedures. Part (a) asks for basic reasoning about 1-tail vs 2-tail tests (testing for 'linear correlation' suggests 2-tail). Part (b) is a routine application: compare the calculated r-value (0.2705) with the critical value from the table (0.3120 for n=40, 2-tail, 5%), state conclusion. No complex calculations or novel insight required—pure procedural application of a standard Stats 1 technique. |
| Spec | 2.05c Significance levels: one-tail and two-tail2.05g Hypothesis test using Pearson's r |
| 1-tail test | 2-tail test | |||
| 5% | 2.5% | 1% | 0.5% | |
| 10% | 5% | 2.5% | 1% | |
| 38 | 0.2709 | 0.3202 | 0.3760 | 0.4128 |
| 39 | 0.2673 | 0.3160 | 0.3712 | 0.4076 |
| \(n\) 40 | 0.2638 | 0.3120 | 0.3665 | 0.4026 |
| 41 | 0.2605 | 0.3081 | 0.3621 | 0.3978 |
Laxmi wishes to test whether there is linear correlation between the mass and the height of adult males.
\begin{enumerate}[label=(\alph*)]
\item State, with a reason, whether Laxmi should use a 1-tail or a 2-tail test. [1]
\end{enumerate}
Laxmi chooses a random sample of 40 adult males and calculates Pearson's product-moment correlation coefficient, $r$. She finds that $r = 0.2705$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Use the table below to carry out the test at the 5% significance level. [5]
\end{enumerate}
Critical values of Pearson's product-moment correlation coefficient.
\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
& \multicolumn{2}{|c|}{1-tail test} & \multicolumn{2}{|c|}{2-tail test} \\
\hline
& 5% & 2.5% & 1% & 0.5% \\
\hline
& & & & \\
\hline
& 10% & 5% & 2.5% & 1% \\
\hline
38 & 0.2709 & 0.3202 & 0.3760 & 0.4128 \\
\hline
39 & 0.2673 & 0.3160 & 0.3712 & 0.4076 \\
\hline
$n$ 40 & 0.2638 & 0.3120 & 0.3665 & 0.4026 \\
\hline
41 & 0.2605 & 0.3081 & 0.3621 & 0.3978 \\
\hline
\end{tabular}
\end{center}
\hfill \mbox{\textit{OCR H240/02 2018 Q11 [6]}}