Hypothesis test of Pearson’s product-moment correlation coefficient
8
For a random sample of ten pairs of values of \(x\) and \(y\) taken from a bivariate distribution, the equations of the regression lines of \(y\) on \(x\) and of \(x\) on \(y\) are, respectively,
$$y = 0.38 x + 1.41 \quad \text { and } \quad x = 0.96 y + 7.47$$
Find the value of the product moment correlation coefficient for this sample.
Using a \(5 \%\) significance level, test whether there is positive correlation between the variables.
For a random sample of \(n\) pairs of values of \(u\) and \(v\) taken from another bivariate distribution, the value of the product moment correlation coefficient is 0.507 . Using a test at the \(5 \%\) significance level, there is evidence of non-zero correlation between the variables. Find the least possible value of \(n\).