Question 7 [4 marks] The number of fixture your team wins in a season can be viewed as the realisation of a Binomial random variable. a) Below you are shown the binomial probabilities of winning less than or equal to x games out of 15 under the null hypothesis, H0 : zTamiX win = 0.5 . Based on this, if you wanted to ensure the probability of incorrectly rejecting the null hypothesis is at most a = 0.05 , what would the critical value for the number of games won be? Assume the alternative hypothesis is the same as you wrote down in 6a). x 0 1 2 3 4 5 6 7 Pr(X S x) 0.0000 0.0005 0.0037 0.0176 0.0592 0.1509 0.3036 0.5000 x 8 9 10 11 12 13 14 15 Pr(X S x) 0.6964 0.8491 0.9408 0.9824 0.9963 0.9995 1.0000 1.0000 b) Based on the win rate of the Tactix in 2022, you are asked to conduct a power study where you will simulate binomial data y N Binomial(15, :rTmiX win ) assuming 7mm\" win = 1/3 . Write R code that would allow you to determine the power of the test