I have a survey with sample size 560 from population of 11,000. There are several questions with Likert Scale response (Very Likely, Likely, neutral, Unlikely, Very Unlikely).

What is the method to test significance that the sample represents the population as a whole?

Also, the population can be orthogonally segmented by Department (Legal, Accounting, Lab1, Lab2) and by Job (Chemist, Biologist, Engineering, Lawyer,. )

The survey recorded the Department and Job of each respondent.

What is the method to compare responses between Departments and Jobs?

Thanks.

best,
--dave