| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Year | 2021 |
| Session | June |
| Marks | 12 |
| Topic | Bivariate data |
| Type | Calculate r from raw bivariate data |
| Difficulty | Standard +0.3 Part (a) requires interpreting a given correlation coefficient and performing a standard hypothesis test using critical values from tables. Part (b) involves calculating r from scratch using the formula with given summaries, requiring careful arithmetic with the removal of one data point. This is a routine Further Maths Statistics question with standard techniques and no novel insight required, making it slightly easier than average. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08b Linear coding: effect on pmcc5.08d Hypothesis test: Pearson correlation |
| Book | A | B | C | D | E | F | G | H | I | J | K | L |
| \(x\) | 0.95 | 0.65 | 0.70 | 0.90 | 0.55 | 1.40 | 1.50 | 0.50 | 1.15 | 0.35 | 0.20 | 0.35 |
| \(y\) | 6.06 | 7.00 | 2.00 | 5.87 | 4.00 | 5.36 | 7.19 | 2.50 | 3.00 | 8.29 | 1.37 | 2.00 |
2 A book collector compared the prices of some books, $\pounds x$, when new in 1972 and the prices of copies of the same books, $\pounds y$, on a second-hand website in 2018.\\
The results are shown in Table 1 and are summarised below the table.
\begin{table}[h]
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | c | c | c | c | c | }
\hline
Book & A & B & C & D & E & F & G & H & I & J & K & L \\
\hline
$x$ & 0.95 & 0.65 & 0.70 & 0.90 & 0.55 & 1.40 & 1.50 & 0.50 & 1.15 & 0.35 & 0.20 & 0.35 \\
\hline
$y$ & 6.06 & 7.00 & 2.00 & 5.87 & 4.00 & 5.36 & 7.19 & 2.50 & 3.00 & 8.29 & 1.37 & 2.00 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Table 1}
\end{center}
\end{table}
$$n = 12 , \Sigma x = 9.20 , \Sigma y = 54.64 , \Sigma x ^ { 2 } = 8.9950 , \Sigma y ^ { 2 } = 310.4572 , \Sigma x y = 46.0545$$
\begin{enumerate}[label=(\alph*)]
\item It is given that the value of Pearson's product-moment correlation coefficient for the data is 0.381 , correct to 3 significant figures.
\begin{enumerate}[label=(\roman*)]
\item State what this information tells you about a scatter diagram illustrating the data.
\item Test at the $5 \%$ significance level whether there is evidence of positive correlation between prices in 1972 and prices in 2018.
\end{enumerate}\item The collector noticed that the second-hand copy of book J was unusually expensive and he decided to ignore the data for book J.
Calculate the value of Pearson's product-moment correlation coefficient for the other 11 books.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics 2021 Q2 [12]}}