1) Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track runners in the different starting positions. Calculate the chi-square test statistic 2 to test the claim that the number of wins is uniformly distributed across the different starting positions. The results are based on 240 wins. Starting Position 1 2 3 4 5 6 Number of Wins 36 45 44 33 50 32

2) A coffeehouse wishes to see if customers have any preference among 5 different brands of coffee. A sample of 197 customers provided the data below. Calculate the chi-square test statistic 2 to test the claim that the distribution is uniform. Brand 1 2 3 4 5 Customers 55 30 18 62 32

3) Find the critical value F0 for a one-tailed test using = 0.01, d.f.N = 3, and d.f.D = 20.

4) Find the critical value F0 for a two-tailed test using = 0.02, d.f.N = 5, and d.f.D = 10.

5) A random sample of 160 car crashes are selected and categorized by age. The results are listed below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the 26-45 group, 31% for the 45-65 group, and 12% for the group over 65. Calculate the chi-square test statistic 2 to test the claim that all ages have crash rates proportional to their driving rates. Age Under 26 26 - 45 46 - 65 Over 65 Drivers 66 39 25 30

6) A medical researcher wishes to try three different techniques to lower blood pressure of patients with high blood pressure. The subjects are randomly selected and assigned to one of three groups. Group 1 is given medication, Group 2 is given an exercise program, and Group 3 is assigned a diet program. At the end of six weeks, each subjects blood pressure is recorded. Find the critical value F0 to test the claim that there is no difference among the means. Use = 0.05. Group 1 Group 2 Group 3 11 8 8 12 3 12 13 2 4 15 5 4 9 4 9 8 0 6 7) A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins and different sports. A random sample of 526 games is selected and the results are given below. Find the expected frequency for E2,2 to test the claim that the number of home team and visiting team wins are independent of the sport. Round to the nearest tenth if necessary. Football Basketball Soccer Baseball Home Teams Wins 38 153 27 85 Visiting Team Wins 32 96 18 77