Extracting hypotheses and their supporting statistical evidence from full-text scientific articles is central to the synthesis of empirical findings, but remains difficult due to document length and the distribution of scientific arguments across sections of the paper. The work studies a sequential full-text extraction setting, where the statement of a primary finding in an article's abstract is linked to (i) a corresponding hypothesis statement in the paper body and (ii) the statistical evidence that supports or refutes that hypothesis. This formulation induces a challenging within-document retrieval setting in which many candidate paragraphs are topically related to the finding but differ in rhetorical role, creating hard negatives for retrieval and extraction. Using a two-stage retrieve-and-extract framework, we conduct a controlled study of retrieval design choices, varying context quantity, context quality (standard Retrieval Augmented Generation, reranking, and a fine-tuned retriever paired with reranking), as well as an oracle paragraph setting to separate retrieval failures from extraction limits across four Large Language Model extractors. We find that targeted context selection consistently improves hypothesis extraction relative to full-text prompting, with gains concentrated in configurations that optimize retrieval quality and context cleanliness. In contrast, statistical evidence extraction remains substantially harder. Even with oracle paragraphs, performance remains moderate, indicating persistent extractor limitations in handling hybrid numeric-textual statements rather than retrieval failures alone.