Advice on statistically viable sample size

Hello Everyone!

I'm new to statistics and sizing samples. this is not really a calculation question but would like some advice on our current situation and if there are any calculations available or reference material that can be used to support and show evidence to our decision to use 25 samples for our audit.

I work for an auditing company, and my boss is trying to justify a sample we are auditing is statistically viable.

We have a number of contracted companies under our portfolio, and have decided to audit these companies as part of their on going compliance in their usage of our IT products. These companies submit requests on behalf of customers. depending on the company their could be between 10 - 1000 submissions per day.

For our first audit
- we audited 10 companies. each company was required to upload supporting documents for 25 submissions.
- each submissions is checked against 25 different criteria's
- we have a 1% adjustment for human error for all 25 submissions
- so with 25 submissions against 25 essential criteria- there is a total of 675 Criteria they could possibly get incorrect for the 1company.
- with 1 % adjustment we allow for 6 errors out of 675 total errors for the 1 company.

My boss and I are wanting to justify and show come evidence to senior staff that checking 25 submissions against 25 criteria is a good sample size as they are stating it is too small. (we do know bigger sample sizes show better results, but due to time constraints and staffing its hard to do this)

any help would be greatly appreciated.