Hi, everyone:
I'm planning to conduct a mixed-method study that will begin with a questionnaire followed by qualitative interviews. I have a population of around 200 students, and I would like to determine the optimal sample size for both the questionnaire and the interviews. How many students should I select for the questionnaire, and how many should I choose for the interviews?
There is nothing about using mixed methods that affects your sample size in either the qualitative or the quantitative portion of your study. For the quantitative portion, you can use any of the sample size calculators that you can find with a Google search. For the qualitative portion, the classic recommendation would be to rely on saturation as your criterion.
You can use the Krejcie and Morgan formula to determine the sample size based on the size of the population/universe
Article Determining Sample Size for Research Activities
In fact, there is a table that has been generated using this formula- https://www.semanticscholar.org/paper/Determining-Sample-Size-for-Research-Activities-Krejcie-Morgan/de62bfbd044784fe0e60e8a11c1de959b6a7f4bd/figure/0
The sample size for both the quantitative and qualitative parts depend on your methodologies and methods. For example, 200 might/probably will be insufficient if you wanted to conduct EFA -> CFA, SEM, and some other methods (again, depends on number of variables and observations, etc.). The same can be said for qualitative. There is extensive research most researchers either follow general rules of thumb or pick nice round numbers. As for saturation, that also depends on what you wish to accomplish and what you will mean by it (plus, do you have a method for saturation or do you simply make a claim?). Some researchers do not seek saturation, so you must clarify your aims. A great recommendation is decide on a plan, and if possible, be flexible.
200 is not a large population. Why not take all of them into your quant survey and then see what segmentation you see in the results to determine your interview cohort? That way you can use the interviews to explore the differences you see in the quant. If for instance gender and geography cause variation in the quant responses, sample the interviews using these variables.
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