9 The land areas \(x\) (in suitable units) and populations \(y\) (in millions) for a sample of 8 randomly chosen cities are given in the following table.
| Land area \(( x )\) | 1.0 | 4.5 | 2.4 | 1.6 | 3.8 | 8.6 | 7.5 | 6.5 |
| Population \(( y )\) | 0.8 | 8.4 | 4.2 | 1.6 | 2.2 | 10.2 | 4.2 | 5.2 |
$$\left[ \Sigma x = 35.9 , \Sigma x ^ { 2 } = 216.47 , \Sigma y = 36.8 , \Sigma y ^ { 2 } = 244.96 , \Sigma x y = 212.62 . \right]$$
- Find, showing all necessary working, the value of the product moment correlation coefficient for this sample.
- Using a \(1 \%\) significance level, test whether there is positive correlation between land area and population of cities.
The land areas and populations for another randomly chosen sample of cities, this time of size \(n\), give a product moment correlation coefficient of 0.651 . Using a test at the \(1 \%\) significance level, there is evidence of non-zero correlation between the variables. - Find the least possible value of \(n\), justifying your answer.