When sampling without replacement, the rule of thumb for treating observations as independent is that the sample size should not exceed 10% of the total population. This is known as the "10% condition."

Given:

• Population size: $N = 400$

To maintain the independence assumption, the sample size $n$ must satisfy:

$n \leq 0.10 \times N$

Substituting the given population size:

$n \leq 0.10 \times 400 = 40$

Thus, Mark can sample up to 40 students without replacement and still reasonably treat the observations as independent.

Would you like further details or explanations on this?

Here are some related questions for further exploration:

1. Why is the 10% condition important in hypothesis testing?
2. How does sampling without replacement affect hypothesis testing assumptions?
3. What other conditions are necessary for a hypothesis test besides independence?
4. What are the differences between sampling with and without replacement?
5. How would increasing the population size affect the sample size for independence?

Tip: Always check whether other assumptions (e.g., normality, randomness) are met in addition to the 10% condition when performing a hypothesis test.