The overall distance traveled by a golf ball is tested by hitting the ball with Iron Byron, a mechanical golfer with a swing that is said to emulate the legendary champion, Byron Nelson. Ten randomly selected balls of two different brands are tested and the overall distance measured. The data follow:
Brand 1: $275,286,287,271,283,271,279,275,263,267$
Brand 2: $258,244,260,265,273,281,271,270,263,268$
a) Which procedure is the most appropriate, matched pairs $T$ or two sample T? Explain
b) Find a $95 \%$ confidence interval for the difference of the mean.
c) Use the four-step procedure to carry out a hypothesis test to determine whether the mean overall distance for brand 1 and brand 2 are different?