p value and hypothesis testing

Question

In a random sample of 99 games the home team won 57 games. Test the null hypothesis That home team wins one half of all games against the alternative that the home team wins a majority games.

How can I calculate p value and find the threshold of significance level??

Do I reject the null hypothesis(H0) if p-P/root(p(1-p)/n) > Zp

So that p value is P(Zp> )?

Answer 1

You have

$H_0: p=0.5$

$H_A: p > 0.5$

$T=\frac{\frac{57}{99}-0.5}{\sqrt{0.5\cdot 0.5}}\cdot \sqrt{99}$

If $|T|>z_{1-\alpha }$, then you reject $H_0$.

$\alpha$ is the significance level.

The value of $z_{1-\alpha }=z_p$ can be found at a table of the standard normal distribution, e.g here