Standard +0.3 This is a standard two-sample t-test with summary statistics requiring calculation of sample means and variances, then applying the pooled t-test formula. While it involves multiple computational steps and understanding of hypothesis testing framework, it's a routine application of a standard procedure with no conceptual surprises—slightly easier than average due to being a textbook application, but the computational burden and multiple steps keep it near average difficulty.
8 Weekly expenses claimed by employees at two different branches, \(A\) and \(B\), of a large company are being compared. Expenses claimed by an employee at branch \(A\) and by an employee at branch \(B\) are denoted by \(\\) x\( and \)\\( y\) respectively. A random sample of 60 employees from branch \(A\) and a random sample of 50 employees from branch \(B\) give the following summarised data.
$$\Sigma x = 6060 \quad \Sigma x ^ { 2 } = 626220 \quad \Sigma y = 4750 \quad \Sigma y ^ { 2 } = 464500$$
Using a \(2 \%\) significance level, test whether, on average, employees from branch \(A\) claim the same as employees from branch \(B\).
8 Weekly expenses claimed by employees at two different branches, $A$ and $B$, of a large company are being compared. Expenses claimed by an employee at branch $A$ and by an employee at branch $B$ are denoted by $\$ x$ and $\$ y$ respectively. A random sample of 60 employees from branch $A$ and a random sample of 50 employees from branch $B$ give the following summarised data.
$$\Sigma x = 6060 \quad \Sigma x ^ { 2 } = 626220 \quad \Sigma y = 4750 \quad \Sigma y ^ { 2 } = 464500$$
Using a $2 \%$ significance level, test whether, on average, employees from branch $A$ claim the same as employees from branch $B$.
\hfill \mbox{\textit{CAIE FP2 2014 Q8 [9]}}