Are the economies that became member states of the European Union after 2004 catching up to the older members? The file EUGDP2017 contains real GDP growth rates in 2017 for the \(28 \mathrm{EU}\) countries, along with their status according to the date on which they became EU members (old - before 2004, new - 2004 and after).

a. At the 0.05 level of significance, is there evidence of a difference in the variability of the GDP growth rates between the two groups of member states?

b. Determine the \(p\)-value in (a) and interpret its meaning.

c. What assumptions do you need to make in (a) about the two populations in order to justify your use of the \(F\) test?

d. Based on the results of (a) and (b), which \(t\) test defined in Section 10.1 should you use to compare the mean growth rates of the two groups of member states?