Paired t-test using averages


I would really appreciate if you could help me with my research design for my thesis.

I am investigating a group of companies in terms of % of female employees compared to the respective industry average. The problem is that the companies are from different industries, and of course some industries have generally less female employees than others.

So what I was planning to do is pair each company's percentage with the industry average percentage (eg Software company paired with IT industry average, Food company with food industry average etc.) and do a paired t-test.

Is this design flawed? I am worried since I am using the industry averages as a comparison sample without considering the variance within the respective industries...

Thank you!