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. Assuming that the population variances from both types of members are equal, is there an evidence of a difference in the mean growth rates? (Use \(\alpha=0.05\).)

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

c. What other assumption is necessary in (a)?

d. Assuming that the population variances from both groups of members are equal, construct and interpret a \(95 \%\) confidence interval estimate of the difference between the population means of the two groups.

e. What conclusions can you reach about the growth rates in 2017 of the two groups of member states?