Here was a "self-proclaimed" penalty kicker. To test whether his skills were genuine, he was asked to kick a penalty kick and succeeded five times in a row. So, can we say that the PKer's skills are genuine?
To this question, some will answer, "You put it in five times in a row, so it must be real", while others will say, "No, no, you can't tell with just five times, you might get it wrong on the sixth time." It's a matter of opinion, isn't it?
This is objectively determined using statistics, a method called hypothesis testing. First, the hypothesis (named H0)
H0: This PK craftsman has no skills. We will formulate the following. If we can explain that this hypothesis is wrong, we can
H1: This PK craftsman has skills. This means that. (We name this state of affairs H1)
Now, it is time to test whether this H0 is correct using the hypothesis testing method. Now, to begin with, the probability of scoring five consecutive penalty kicks without technology is
(12)5=132=0.03125 which gives a probability of 3.125%.
the PK craftsman did not have the skills, then this approximately 3% chance of success would be a 'fluke'. It is not impossible, but it is a very low probability.
By me thinking "that's a very low probability, so hypothesis H0 would be wrong", hypothesis H1 would be correct and the PK craftsman's skill would be recognised.
But here is where the problem arises. I have taken the liberty of deciding that hypothesis H0 is wrong, but there is a 3.125% probability that it is correct.
Can I really decide on my own that "the probability of being right is only 3%, so it's wrong!" Can I decide on my own that it is wrong because the probability of being right is only 3%?
Of course not. In statistical hypothesis testing, this criterion is named the significance level α and is determined before any calculations are made. Usually, 5% or 1% (α = 0.05 or a = 0.01) is used. In this case, if the significance level is 5%, H0 can be judged to be wrong. However, if the significance level is 1%, H0 cannot be wrong.
