Problem

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 of this species from country $X$ and a random sample of 80 birds of this species from country $Y$. She records their masses in kg, $x$ and $y$, respectively. Her results are summarised as follows.

$\sum x = 75.5 \qquad \sum x^2 = 115.2 \qquad \sum y = 116.8 \qquad \sum y^2 = 172.6$

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 $\mu_x > \mu_y$. State your conclusion in the context of the question.