7. PGA Golf Scores 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. At a _ 0.05, is there evidence of a difference in mean scores for the two days? Golfer 1 2 3 4 5 6 7 8 Thursday 67 65 68 68 68 70 69 70 Friday 68 70 69 71 72 69 70 70 8. A composition teacher wishes to see whether a new grammar program will reduce the number of grammatical errors her students make when writing a two-page essay. The data are shown here. At a _ 0.025, can it be concluded that the number of errors has been reduced? Student 1 2 3 4 5 6 Errors before 12 9 0 5 4 3 Errors after 9 6 1 3 2 3 9. A survey found that 83% of the men questioned preferred computer-assisted instruction to lecture and 75% of the women preferred computer-assisted instruction to lecture. There were 100 individuals in each sample. At a _ 0.05, test the claim that there is no difference in the proportion of men and the proportion of women who favor computer-assisted instruction over lecture. Find the 95% confidence interval for the difference of the two proportions. 10. In a sample of 50 men, 44 said that they had less leisure time today than they had 10 years ago. In a sample of 50 women, 48 women said that they had less leisure time than they had 10 years ago. At a 0.10 is there a difference in the proportion? Find the 90% confidence interval for the difference of the two proportions. Does the confidence interval contain 0? Give a reason why this information would be of interest