2. An economist suggested the rate of unemployment and the rate of wage inflation are independent. Amy sets about investigating this suggestion. She collects unemployment data and wage inflation data from a random sample of regions in the UK and decides that it is appropriate to carry out a significance test on Pearson's product moment correlation coefficient.
Amy's summary statistics for percentage unemployment, \(x\), and percentage wage inflation, \(y\), are shown below.
$$\begin{array} { l l l }
\sum x = 62 \cdot 8 & \sum y = 19 \cdot 4 & n = 10
\sum x ^ { 2 } = 413 \cdot 44 & \sum y ^ { 2 } = 46 \cdot 16 & \sum x y = 113 \cdot 16
\end{array}$$
- Calculate Pearson's product moment correlation coefficient for these data.
- Carry out Amy's test at the \(5 \%\) level of significance and state whether the economist's suggestion is reasonable.
Amy also collects unemployment data and wage inflation data from a random sample of 10 regions in Spain and calculates Pearson's product moment correlation coefficient to be - 0.2525 .
- Should this change Amy's opinion on the economist's suggestion above? What could she do to improve her investigation?
- What assumption has Amy made in deciding that it is appropriate to carry out a significance test on Pearson's product moment correlation coefficient?