I'm having a hard time understanding how to complete a part of a question from an assignment. The question states:
Suppose we have 103 students in our class. Suppose all students collect a random sample of size 2500 from the same population, and each student constructs a 95% CI for $\beta_1$ from his/her own data. What is the expectation for number of students who will miss the true value of $\beta_1$? Note that the number of students who miss the true value of $\beta_1$ follows a binomial distribution.
Previously I had to find a 95% CI for this $\beta_1$ from a T-distribution. However since I figured that each students CI might have different values, then I obviously wouldn't be using my data to solve this problem.
Based on the note at the end, I assumed I could get the answer by doing:
$E(X) = np$ where $n = 103$. But then I don't know how to calculate the $p$ value to get the expected value. And I still don't know if this is even what the question is asking me.
$p=5\%$ since that's the probability each student has for the true value of $\beta1$ lying outside his CI. $E(X) = 103(0.05)$.