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]
| 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 |
\captionsetup{labelformat=empty}
\caption{Table 1}
\end{table}
$$n = 12 , \sum x = 9.20 , \sum y = 54.64 , \sum x ^ { 2 } = 8.9950 , \sum y ^ { 2 } = 310.4572 , \sum x y = 46.0545$$
- It is given that the value of Pearson’s product-moment correlation coefficient for the data is 0.381, correct to 3 significant figures.
- State what this information tells you about a scatter diagram illustrating the data.
- Test at the \(5 \%\) significance level whether there is evidence of positive correlation between prices in 1972 and prices in 2018.
- 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.