| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2021 |
| Session | May |
| Marks | 6 |
| Topic | Hypothesis test of Pearson’s product-moment correlation coefficient |
| Type | Two-tailed test for any correlation |
| Difficulty | Easy -1.2 This is a straightforward hypothesis testing question requiring only standard recall and table lookup. Part (a) asks for basic understanding of 1-tail vs 2-tail tests (testing 'whether there is correlation' clearly indicates 2-tail). Part (b) involves comparing a given r-value to a critical value from a provided table—purely mechanical with no problem-solving or conceptual challenge beyond routine application. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
| \cline{2-5} |
| \(5 \%\) | \(2.5 \%\) | \(1 \%\) | ||
| \(10 \%\) | \(5 \%\) | \(2.5 \%\) | \(1 \%\) | ||
| 38 | 0.2709 | 0.3202 | 0.3760 | 0.4128 | ||
| 39 | 0.2673 | 0.3160 | 0.3712 | 0.4076 | ||
| 40 | 0.2638 | 0.3120 | 0.3665 | 0.4026 | ||
| 41 | 0.2605 | 0.3081 | 0.3621 | 0.3978 |
3. 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.
Laxmi chooses a random sample of 40 adult males and calculates Pearson's product-moment correlation coefficient, $r$. She finds that $r = 0.2705$.
\item Use the table below to carry out the test at the $5 \%$ significance level.
Critical values of Pearson's product-moment correlation coefficient.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\cline{2-5}
& \begin{tabular}{ c }
1-tail \\
test \\
\end{tabular} & $5 \%$ & $2.5 \%$ & $1 \%$ \\
\hline
\begin{tabular}{ c }
2-tail \\
test \\
\end{tabular} & $10 \%$ & $5 \%$ & $2.5 \%$ & $1 \%$ \\
\hline
38 & 0.2709 & 0.3202 & 0.3760 & 0.4128 \\
\hline
39 & 0.2673 & 0.3160 & 0.3712 & 0.4076 \\
\hline
40 & 0.2638 & 0.3120 & 0.3665 & 0.4026 \\
\hline
41 & 0.2605 & 0.3081 & 0.3621 & 0.3978 \\
\hline
\end{tabular}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Statistics 2021 Q3 [6]}}