Question

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 nextInne is Lane 2, and so on until the outermostlane, Lane 6. The table displays the starting positions for the winners of 240 competitions. Find the rejection region used to test the claim that the probability of winning is the same regardless of starting position. Use 0.05. The results are based on 240 wins. Starting Position Number of Wins 1 2 3 4 5 33 44 32 50 45 36 OA /> 12.833 OB />9236 OC /> 11.070 OD />15.086

Answer 1

Summary;

Here rejection region is (C) $\chi$ ² > 11.070
calculation, * statistical table starting position (0;-2;3460;-2134 1:225 49 16 64 observed | Expected frequencies frequencies (0;) (ei) 33 40 44 40 32 40 so 40 45 40 36 40 240 240 2 3 4 5 0:4 1:6 100 2.5 25 0.625 16 04 6 Total 6.75 É co; -e;)? Here, K= 6, p = 0 ~ K-p-1 = 5 Now, Test statistic, x² (calculated value) x² 6-75 Now critical value at 5 % level of significance is Xx-p-1a = X6-0-1,0.05 こ S X5,oos 11:070 (table value) * Result: Therefore rejection region is © X > 11.070 Here x3 = 6:75 x 0.05 = 11.070 Accept Ho