1. **Problem Statement:** Calculate the total sample size in a multistage stratified sampling design where two universities are selected, each with 16 colleges, and from each college, 48 students are sampled. 2. **Formula Used:** The total sample size $n$ is given by the sum over all universities: $$n=\sum_{i=1}^k (C_i \times S_{ci})$$ where $k$ is the number of universities, $C_i$ is the number of colleges in university $i$, and $S_{ci}$ is the number of students sampled per college in university $i$. 3. **Given Values:** - Number of universities: $k=2$ - Colleges per university: $C_1 = C_2 = 16$ - Students per college: $S_{c1} = S_{c2} = 48$ 4. **Calculation:** $$n = (16 \times 48) + (16 \times 48)$$ $$n = 768 + 768$$ $$n = 1536$$ 5. **Interpretation:** The total sample size across both universities is 1536 undergraduate students. 6. **Additional Notes:** The sampling is stratified by gender and academic year within each college, ensuring balanced representation. **Final Answer:** $$n = 1536$$ undergraduate students.