Question

please complete A and B

Chi-square Problems 1. The National Highway Traffic Safety Administration publishes reports about motorcycle fatalities and helmet use. The distribution below shows the proportion of fatalities by location of injury for motorcycle accidents. Location of Injury Multiple location Head Proportion 0.57 0.31 Neck 0.03 Thorax 0.06 Abdomen/Lumbar/Spine 0.03 Data below show the location of injury and fatalities for 2068 riders not wearing a helmet. Location of Injury Multiple location Head Number 1036 864 38 83 Neck Thorax Abdomen/Lumbar/Spine 47 A. Does the distribution of fatal injuries for riders not wearing helmet follow the distribution of all riders? Use 5% level of significance. B. In the context of this problem, describe in your own words the Type I and Type II errors associated with the test.

Answer 1

Ahsuar: (A) The following null and alfermlive hy Pothesel need to be tated tHo :P -0 54, P2 0-31,f3 :0.03 , Pu =0-06, P5 = 0-03 th Some of fe population differe frem the valuei slated in the ml hypothelis Inwords Distribution of fatal injuriel for iders ot wearing the helmels doe follaw the distribuution or all riders 4 distributin on fataf injuriel for Biders not wraning the helmett doce nol af all riders. Ho distribulion follow the (fofe )"{fe (1036-1148.76)7 Il 4846-:1-0 Categorie obserred Nultiple location hepected 10 36 I148.76 Head (664-641.08) 141o - 47.515 641.08 Neck (38-62 04/0 38 NOGSXO 03 = 62.04 : १'35 Thorax 83 0684006= /24. - 13 -601 ২५.०৪ Abdamen (47-62.04)76204: NO68*O-03: 63.04. 3.6५6 121. 367 ac6s Sum = statistic is compuled as follows: The chi-squared =17 29+11.515+ 9.315+ 13-601 + 3.646 = I21. 367 df . 5-1 =4 Scanned with CamScanner

Gitical chi-square value =9.488<121.36t ie we Can can Say that distribulign reject Ho and bence of Cwe -fatal injuriel -for riders not wearing the helmet doel not follow the distribution of all niders. BType i Eror: Rejecting the ull hypothesi's when it is lin fact true · 1.e., accepting that the di'stribution of fatal injuniel for nicers not weaning the helmates doer not follow the di'stribution of all nidery when they actually do. ype II Etror! Failling to reject the hull hypother's when it is in tact' falie. ie. accepting that the di'stribution of fatal injuries for del follow the distribution of riders not weating the helmatu all riderd when they actually do rof. Scanned with CamScanner