The FIFA World Cup was one of the biggest sporting events of 2018. The file WC2018Players contains data of the players of the 32 teams that qualified for the event. A dummy variable is included to indicate whether a player is also a captain.

a. Assuming the population variance of the ages of captains and non-captains are equal, is there evidence of a difference in the mean ages of captains and non-captains? (Use \(\alpha=0.05\).)

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

c. Assuming that the population variances from both captains and non-captains are equal, construct and interpret a 95\% confidence interval estimate of the difference between the population mean age of captains and non-captains.