The results of a survey made to determine whether the age of

The results of a survey made to determine whether the age of a driver twenty-one years of age or older has any effect on the number of automobile accidents in which the driver is involved (including all minor accidents) are shown in the table below. Using ? = 0.05, test the hypothesis that the number of accidents is independent of the age of the driver.

Age of Driver 21-303140 41-50 51-606170 786 748 821 60 25 10 720 672 74 50 16 more than 2

Solution

Ho: the number of accidents is independent of the age of the driver. Ha:the number of accidents is n\'t independent of the age of the driver. Col 1   Col 2   Col 3   Col 4   Col 5   Total   Row 1 Observed   748 821 786 720 672 3747 Expected   770.13 818.37 772.81 720.99 664.70 3747.00 O - E   -22.13 2.63 13.19 -0.99 7.30 0.00 (O - E)² / E   0.64 0.01 0.23 0.00 0.08 0.95 Row 2 Observed   74 60 51 66 50 301 Expected   61.87 65.74 62.08 57.92 53.40 301.00 O - E   12.13 -5.74 -11.08 8.08 -3.40 0.00 (O - E)² / E   2.38 0.50 1.98 1.13 0.22 6.20 Row 3 Observed   31 25 22 16 15 109 Expected   22.40 23.81 22.48 20.97 19.34 109.00 O - E   8.60 1.19 -0.48 -4.97 -4.34 0.00 (O - E)² / E   3.30 0.06 0.01 1.18 0.97 5.52 Row 4 Observed   9 10 6 5 7 37 Expected   7.60 8.08 7.63 7.12 6.56 37.00 O - E   1.40 1.92 -1.63 -2.12 0.44 0.00 (O - E)² / E   0.26 0.46 0.35 0.63 0.03 1.72 Total Observed   862 916 865 807 744 4194 Expected   862.00 916.00 865.00 807.00 744.00 4194.00 O - E   0.00 0.00 0.00 0.00 0.00 0.00 (O - E)² / E   6.57 1.03 2.56 2.94 1.30 14.40 ^2 Test Statistic =14.4 ^2 degrees of freedom = ( r-1 ) * (c-1) = 3 * 4 = 12, ^2 tab at 0.05 LOS = 21.03 ^2 p_value =0.0255 | ^2 tab | > | ^2 cal | i.e. Failed to Reject Ho the number of accidents is independent of the age of the driver.