Use the normal approximation to carry out a test of the hypothesis that both models are equally good at predicting games. What is the conclusion of your test?
\( n = n_{11} + n_{12} + n_{21} + n_{22} \)
\( p_{12} = n_{12}/n \) \( p_{21} = n_{21}/n \)
\( H_0: p_{12} = p_{21} \) \( H_1: p_{12} \neq p_{21} \)
Because \( n_12 + n_21 > 25 \), we can perform chi square test:
\[ \chi^2_{df=1} = \frac{(|n_{21} - n_{12}|-0.5)^2}{n_{21}+n_{12}} = \frac{(|24 - 27|-0.5)^2}{24 + 27} = 0.1225 \]
For the single sided test, p-value corresponting to this test statistics is 0.2737, but for this double sides, this is 0.5474. Thus we can conclude that the hypothesis testing is insignificant. We fail to reject the null hypothesis. Thus we can conclude that the two models do not perform better than the other significantly.