The weekly salaries of employees at two large electronics companies, \(A\) and \(B\), are being compared. The weekly salaries of an employee from company \(A\) and an employee from company \(B\) are denoted by \(\$ x\) and \(\$ y\) respectively. A random sample of 50 employees from company \(A\) and a random sample of 40 employees from company \(B\) give the following summarised data.
\[\Sigma x=5120 \quad \Sigma x^{2}=531000 \quad \Sigma y=3760 \quad \Sigma y^{2}=375135\]
(i) The population mean salaries of employees from companies \(A\) and \(B\) are denoted by \(\$ \mu_{A}\) and \(\$ \mu_{B}\) respectively. Using a \(5 \%\) significance level, test the null hypothesis \(\mu_{A}=\mu_{B}\) against the alternative hypothesis \(\mu_{A} \neq \mu_{B}\).
(ii) State, with a reason, whether any assumptions about the distributions of employees' salaries are needed for the test in part (i).