Question
The state transportation department recently conducted a study of motorists in Idaho. Two main factors of interest were whether the vehicle was insured with liability insurance and whether the driver was wearing a seat belt. A random sample of 100cars was stopped at various locations throughout the state. The data are in the file called Liabins. The investigators were interested in determining whether seat belt status is independent of insurance status. Conduct the appropriate hypothesis test using a 0.05 level of significance and discuss your results.
Driving Citations Vehicle Year Driver Sex Driver Age Seat Belt Status Law Knowledge Employment Status Year In State Registered Vehicles Years Education Insurance Certificate Status Insurance Status 0 70 1 29 3 1 1 4 2 12 1 1 0 79 2 24 2 1 2 17 1 10 2 1 0 87 1 50 2 1 2 0 1 12 1 1 0 92 1 64 2 2 2 37 1 12 1 1 0 87 2 18 2 1 1 9 0 11 1 1 0 97 2 18 2 1 2 10 0 11 1 1 0 91 1 52 1 1 2 52 3 17 1 1 0 89 2 38 2 1 1 7 1 2 1 1 2 97 1 31 1 1 1 30 2 12 1 1 0 92 1 58 2 1 1 57 2 9 1 1 1 84 1 69 2 1 2 4 2 10 1 1 0 88 2 45 2 1 1 12 0 13 2 1 0 96 1 35 1 1 1 10 3 14 2 1 0 90 2 42 2 1 1 13 3 12 1 1 0 95 2 22 1 1 1 21 1 12 1 1 1 97 2 20 1 1 2 17 1 12 1 1 0 89 1 36 1 1 1 35 3 12 1 1 0 10 1 23 2 0 1 11 2 12 2 1 0 92 1 55 1 1 1 45 1 13 2 1 0 78 2 61 2 1 2 7 3 16 2 1 1 97 1 68 1 1 2 9 2 12 1 1 0 96 2 65 1 1 2 2 1 18 1 1 0 90 1 61 0 1 1 59 1 16 2 1 0 96 1 37 2 1 1 25 2 14 1 1 1 86 1 38 2 1 2 37 1 14 2 1 0 89 2 49 2 1 1 48 2 13 1 1 5 89 1 21 2 1 1 20 1 12 1 1 0 87 2 39 1 1 2 1 3 12 2 1 2 84 1 38 2 1 1 21 2 1 1 1 0 88 1 18 2 1 2 17 1 10 2 1 1 10 1 27 1 1 1 2 1 10 2 0 0 94 2 58 2 1 1 57 2 12 1 1 0 88 1 26 2 1 2 10 2 10 1 1 0 92 1 37 1 1 2 9 2 12 2 1 1 89 2 31 2 1 2 9 1 15 2 1 1 95 1 56 2 1 1 55 2 10 1 1 1 82 1 18 3 1 1 16 1 12 1 1 0 88 2 61 2 1 2 60 1 12 2 1 0 88 1 42 2 1 1 17 3 14 2 1 0 94 2 41 1 1 1 26 4 12 2 1 2 89 1 19 2 1 1 14 1 12 1 1 0 89 1 55 2 3 2 30 2 6 2 1 0 93 2 67 2 1 1 66 2 12 1 1 0 88 2 50 1 1 2 49 4 18 1 1 0 89 1 48 2 1 2 47 2 8 2 1 0 78 1 49 2 1 1 46 7 12 1 1 0 85 1 38 2 1 1 11 3 12 2 1 0 87 1 27 2 1 1 26 1 12 2 1 1 94 2 22 1 1 1 21 1 13 1 1 1 96 2 23 2 1 1 20 2 13 1 1 3 91 1 20 2 1 1 18 1 12 2 0 0 91 2 42 1 1 1 11 4 17 1 1 0 10 1 24 2 1 1 6 0 1 1 1 0 83 2 70 2 1 2 69 1 14 1 1 0 93 2 42 2 1 2 36 3 12 1 1 1 84 1 29 2 1 1 28 1 16 1 1 0 94 1 50 2 1 1 39 2 9 1 1 0 96 2 45 2 0 1 40 1 12 2 1 1 97 2 62 1 1 2 60 3 11 1 1 0 10 1 18 2 1 1 16 3 12 1 1 0 90 2 38 2 1 1 27 2 13 1 1 0 69 1 66 2 1 2 65 5 13 1 1 0 83 2 43 1 1 2 9 4 16 1 1 0 87 2 19 2 2 1 3 1 10 2 1 0 85 1 65 2 1 2 64 6 12 1 1 0 91 1 62 2 1 1 40 2 8 1 1 0 89 1 72 1 1 1 68 4 8 1 1 0 86 1 28 2 1 1 27 2 16 2 1 0 96 2 44 2 1 1 43 1 12 1 1 0 96 1 80 2 1 2 75 1 18 2 1 0 85 2 48 2 1 1 47 1 12 1 0 1 82 1 27 2 1 2 26 2 12 1 1 0 96 2 41 2 1 2 25 3 9 1 1 0 10 1 29 2 1 1 27 2 12 1 1 1 88 1 44 2 1 1 43 3 12 1 1 0 87 1 38 2 1 1 37 2 15 1 1 0 80 1 19 2 1 2 18 0 12 1 1 5 98 1 31 2 1 1 30 2 16 2 1 1 97 2 36 1 1 2 3 0 12 1 1 0 92 1 33 2 1 1 32 2 10 1 1 0 89 1 83 2 1 2 65 4 8 1 1 0 96 1 45 2 1 1 44 2 15 2 1 0 90 2 79 1 1 2 1 1 13 2 0 0 97 2 39 2 2 1 13 3 14 1 0 0 10 1 61 2 1 1 39 3 12 1 1 0 81 2 23 2 1 2 12 0 12 2 0 0 83 1 41 1 1 1 35 5 13 1 1 0 96 1 30 1 1 1 14 2 12 1 0 0 87 1 24 2 1 1 21 2 12 1 1 2 86 1 39 1 1 1 3 3 16 1 1 1 88 1 22 1 1 1 19 1 12 2 1 1 95 1 65 1 1 1 64 1 12 1 1 4 81 1 22 1 1 2 21 2 12 2 1 1 10 1 70 3 3 2 45 3 6 2 1 0 76 1 26 2 1 1 25 2 14 1 1 1 84 1 27 2 1 1 3 3 10 1 1 1 90 1 32 2 1 1 6 2 12 1 1 3 88 1 24 2 1 1 15 1 11 1 1 5 70 1 32 2 1 1 15 1 12 2 1 3 75 1 21 2 1 1 5 1 11 1 1
Explanation / Answer
the correlation coefficient is 0.057.. to test the significance of correlation you have to find the t statistic which is t(n-2)= r/sqrt(1-r^2/n-2)
theoretical t value is -0.57
the critical value of t=1.98 at 95% level of significance.
hence we fail to reject the null hypothesis H0: r=0
therefore there is no signifcant correlation between seat belt status and license certificate status.
