A football academy recently hired a new instructor to coach the players. A survey was conducted to determine whether the new instructor is performing well in the academy. For this purpose, two groups of players coached by different instructors were selected. Team A was coached by an older instructor while team B was being coached by the new instructor. Based on the number of goals recorded, 16 out of 25 of goals were scored by team A and team B scored 60 out of 75 goals.

a. Determine a 90% confidence interval for the difference between the proportions of goals scored by both team.

b. Using alpha = 0.10, determine whether team B’s goal rate is better than team A’s.