=(average - 118)/(std.dev/(SQRT(N-1)))You should do a two-tailed test because for all we know having a shorter arm may be advantageous [quicker reaction times? more punches per second?] When you do this, you find that indeed Taylor's arms are significantly different, and longer, than the average. Pretty much everyone in the class got this far correctly - they had been well schooled by myself and are not stupid. They then motored on saying things like "because her arms are much longer than other boxers, she will be at an advantage and so win all her fights". Only one person in the room actually looked at the data to note that 3/20 of these potential opponents had even draggier knuckles than Ms Taylor. The fact that this chap was not the swiftest arrow in the quiver is maybe significant. Quick can sometimes be the antithesis of thoughtful. I was careful to put this across to other sporty students when everyone in the class measured their reaction times.
I picked this as a dataset worthy of analysis because these students are sporty types and the media have uncritically billed Katie Taylor as a Hero of the Republic First Class because she brings home medals 'for' Ireland. That is rather suspicious in my book, surely we want Ireland Inc. to rise in the global consciousness as comely maidens dancing at the cross-roads, Kerrygold butter, fresh caught salmon and U2? Ho hum, in this world, anything that will give the economy a boost is welcomed even if it is the pornography of violence. Two of the sporty types who sat the quiz, both blokes, were with me on this. One correctly answering the question and then gratuitously adding "she's a beast"; another claimed that she had killed a man with a blow to the head but, because the incident had happened in international waters, she couldn't be prosecuted. I think that is rather unlikely but I've written before about boxing and contact sport encephalopathy CSE.
Let's note here the death at aged 29 of Konrad Reuland, an American footballer who played tight end for the Baltimore Ravens and the \Indianapolis Colts. He sustained a brain aneurism which bled out at the end of November, underwent corrective surgery but died anyway. Nobody mentioned CSE in their fulsome obituaries. I wonder if the last few people who 'sacked' him on the playing field feel the teensiest bit guilty?