In a study examining 131 collared flycatcher eggs, researchers measured various characteristics in order to study their relationship to egg size (assayed as egg volume, in \(\mathrm{mm}^{3}\) ). These characteristics included nestling sex and survival. A single pair of collared flycatchers generally lays around 6 eggs per breeding season; laying order of the eggs was also recorded.

(a) Is there evidence at the \(\alpha=0.10\) significance level to suggest that egg size differs between male and female chicks? If so, do heavier eggs tend to contain males or females? For male chicks, \(\bar{x}=1619.95, s=127.54\), and \(n=80\). For female chicks, \(\bar{x}=1584.20, s=102.51\), and \(n=48\). Sex was only recorded for eggs that hatched.

(b) Construct a \(95 \%\) confidence interval for the difference in egg size between chicks that successfully fledged (developed capacity to fly) and chicks that died in the nest. From the interval, is there evidence of a size difference in eggs between these two groups? For chicks that fledged, \(\bar{x}=1605.87, s=126.32\), and \(n=89\). For chicks that died in the nest, \(\bar{x}=1606.91, s=103.46, n=42\).

(c) Are eggs that are laid first a significantly different size compared to eggs that are laid sixth? For eggs laid first, \(\bar{x}=1581.98, s=155.95\), and \(n=22\). For eggs laid sixth, \(\bar{x}=1659.62, s=124.59\), and \(n=20\).