Please help me! I am stuck on this chapter and this question seemed to have it all, so its probably the best one to ask. Thank you!

Let X and Y denote the weights in grams of male and female gallinules. Assume that X is $\displaystyle N(\mu_{x},\sigma^{2}_{x})$ and $\displaystyle Y is N(\mu_{y},\sigma^{2}_{y})$

a) Given n=16 observations of X and m=13 observations of Y, define a test statistic and critical region for testing the null hypothesis $\displaystyle H_{0}: \mu_{x}=\mu_{y}$ against the one-sided alternative hypothesis $\displaystyle H_{1}: \mu_{x} > \mu_{y}$. Let $\displaystyle \alpha=0.01$ and assume variances are equal.

b) Given that $\displaystyle \bar{x}=415.16, s^{2}_{x}=1356.75, \bar{y}=347.40 and s^{2}_{y}=692.21$, calculate the value of the test statistic and make conclusion

c) Test whether the assumption of equal variances is valid. Let $\displaystyle \alpha=0.05$.

d) Despite the fact that $\displaystyle \sigma^{2}_{x}=\sigma^{2}_{y}$ is accepted in part (c), let us say we suspect the equality is not valid. Thus use the test proposed by Welch.

Thank you for even looking! I am ready to tear my hair out trying to understand this entire chapter. I hope someone out there can help me!