t-test should do your job. As a driver for further education, external motivation has a mean $\bar x_{extrinsic} = 5.15$ and internal motivation $\bar x_{intrinsic} = 4.72$. Findings from your sample indicates that students pursue master's degree motivated more extrinsically than intrinsically. Given the sample findings, you can test the hypothesis ($H_0: \mu_{extrinsic} \leq \mu_{intrinsic}$ ; $H_a: \mu_{extrinsic} \gt \mu_{intrisic} $) if the findings are significant for the entire population (all students pursuing master's are motivated more by extrinsic factors than intrinsic ones). Note that one-tailed t-test needs to be used because you are interested in whether one mean is larger than the other, not just in whether they are unequal.
Consider the following t-test assumptions and investigate if your sample holds.
- Continuous variable, i.e., extrinsic and intrinsic scores are measured as quantitative variable
- Each observation is independent of other observations
- variable has a normal distribution