Question

A sample of number of NFL injuries including Concussion, ACL tears, MCL tears and PCL tears from 1999 to 2019 are as follows 1 :

3- Test to check whether the concussion injuries in 2007 are greater than 40% of the total injuries in 2007 or not? (alpha=1%)

PCL Year 1999 2000 2001 2002 2003 2004 2005 2006 MCL 95 102 125 123 98 130 85 93 78 81 145 137 65 102 96 105 83 75 78 2007 2008 2009 2010 NFL Injuries Concussion ACL 185 85 211 71 192 45 215 93 255 65 246 60 203 58 199 55 205 62 241 48 295 71 200 66 245 55 261 62 229 61 206 49 275 59 243 56 281 54 214 57 224 47 88 92 125 122 108 99 115 131 134 140 160 126 144 101 2011 2012 2013 2014 2015 2016 2017 2018 2019 84 91 77 79 83 80 132 109 87

Answer 1

Since the p-value is greater than the 0.01 alpha level, we fail to reject the null hypothesis. We conclude that there is not enough evidence to suggest that  the concussion injuries in 2007 are greater than 40% of the total injuries in 2007.

(3) þ- concession. wy, b = proportion of total injuries that are To test, Hop € 0.40 Hii b > 0.40, 205+62 +125+83 = 475 = Sample 2-1). 0.0) = sample proportion 2015 na aix 0.432, bo = 0.40 x n 475 Test statistic Toa po N(0,1) poll-Po) 1.405. P/2 > 1,405) = 0.08, Plz > Z) P-value