At a recent PGA tournament the Honda Classic at Palm Beach Gardens Florida the following scores were posted for eight randomly selected golfers for two consecutive days Thursday and Friday 4 5 6 7 Golfer Thursday X Friday X ID Hoi Hi Hz 0 H H1 H O Ho X 0 H XD 0 Ho Xo 0 H X 0 65 68 68 70 69 70 70 69 71 72 69 70 70 At a 0 05 is there statistically significant evidence of an increase of scores from Thursday to Friday To find differences take Thursday s score minus Friday s score For instance the difference for Golfer 1 is 1 Golfer 2 is 5 and Golfer 7 is 1 Note that an increase in score causes a negative difference a Which are the null and alternative hypotheses SD 1 Ho XD 0 H X O 67 68 2 3 68 b What are the mean of differences and standard deviation of differences c What is the test statistic Round to 2 decimal places 8 d What is the p value Round to 4 decimal places