Is ‘gay speech’ a thing?
A topic of debate, but still perhaps an understudied topic, is whether it exists a type of speech that specifically indexes sexuality and if so what its features are.
A classic study is Sounding Gay: Pitch Properties in the Speech of Gay and Straight Men by Rudolf Gaudio (https://doi.org/10.2307/455948). There are many more studies that looked at the subject, spanning several features from sibilants to prosody to lexical choices.
For this challenge, you can scout the literature for quantitative results and maybe try and replicate the analysis of an existing study.