Test whether \(p_{1}>p_{2}\). Sample data: \(x_{1}=120, n_{1}=248\), \(x_{2}=139, n_{2}=313\), where \(\alpha=0.010\).

Conduct each test at the \(\alpha\) level of significance by determining

(a) the null and alternative hypotheses,

(b) the test statistic,

(c) the critical value, 

(d) the P-value. 

Assume that the samples were obtained independently using simple random sampling.