A scientist is investigating the masses of birds of a certain species in country \(X\) and country \(Y\). She takes a random sample of 50 birds from country \(X\) and a random sample of 80 birds from country \(Y\). She records their masses in kg, \(x\) and \(y\), respectively. Her results are summarised as follows.

\(\sum x=75.5 \quad \sum x^2=115.2 \quad \sum y=116.8 \quad \sum y^2=172.6\)

The population mean masses of these birds in countries \(X\) and \(Y\) are \(\mu_x\) kg and \(\mu_y\) kg respectively.

Test, at the 5% significance level, the null hypothesis \(\mu_x=\mu_y\) against the alternative hypothesis \(\mu_x\gt \mu_y\). State your conclusion in the context of the question.