By copying strokes made by Tiger Woods in Wachovia Championship, a week later, Gordon Golfer shoots a 70 on round of 18 holes.
Gordon celebrates his good fortune by treating other members of his foursome to round of Guinness at the 19^{th }hole at Quail Hollow, then brags that he played golf as good as Tiger Woods.
One of his buddies responds by saying "Gordon, you drink Guinness better than you play golf. Before you shot that 70, your scores in your last three rounds prior to that were 83, 79, and 80."
Suppose for all parts of this problem that Gordon's golf scores are normally distributed,
(a) Find out the SAMPLE MEAN (x, or x-bar) of the scores Gordon the Golfer made on his last four rounds (i.e., his celebratory round, and the three rounds prior to that).
(b) Find out the SAMPLE STANDARD DEVIATION (s) of the scores Gordon the Golfer made on his last four rounds (determine to the nearest one tenth, or .1).
(c) Employ the appropriate hypothesis test and level of significance (α) of .05 to find out if Gordon the Golfer could claim that his average score for 18 holes is 71 OR LESS or if this claim must be rejected in favor of the alternative that his average score for 18 holes is MORE THAN 71