3. A student is investigating the relationship between different electricity generation methods and cost of electricity in a particular country. The student first checks whether there is any correlation between the cost per unit of electricity, \(x\) euros, and the amount of electricity being generated by wind, \(y \mathrm { GW }\). The data from 30 observations are summarised as follows.
\(n = 30 \quad \sum x = 2.219 \quad \sum y = 357.7 \quad \sum x ^ { 2 } = 0.2368 \quad \sum y ^ { 2 } = 4648 \quad \sum x y = 25.01\)

1. In this question you must show detailed reasoning. Determine the product moment correlation coefficient.
2. Carry out a hypothesis test at the \(5 \%\) level to investigate whether there is any correlation between the cost per unit of electricity and the amount of electricity generated by wind.
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