A book collector compared the prices of some books, \(£x\), when new in 1972 and the prices of copies of the same books, \(£y\), on a second-hand website in 2018.
The results are shown in Table 1 and are summarised below the table.
| 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 |
Table 1
\(n = 12, \Sigma x = 9.20, \Sigma y = 54.64, \Sigma x^2 = 8.9950, \Sigma y^2 = 310.4572, \Sigma xy = 46.0545\)
- 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. [1]
- Test at the 5\% significance level whether there is evidence of positive correlation between prices in 1972 and prices in 2018. [5]
- 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. [2]