(Solved): [Hypothesis testing, p-value] Let a random sample of 1000 college applications is given. In this sa ...

[Hypothesis testing, p-value] Let a random sample of 1000 college applications is given. In this sample, 534 applications were submitted online, while the remaining ones were submitted by post. It is assumed that a half of applications are submitted online. (a) Using p-value, test this hypothesis $\left(H_0:p=0.5\right)$ against the two-sided alternative $(H_A:p\ne$ $0.5)$ at $5\%$ and $1\%$ significance level. (b) Using p-value, test the same null against a one-sided alternative $\left(H_A:p>0.5\right)$ at $5\%$ and $1\%$ significance level.