I have a question about how to calculate the confidence interval for the sum of means from different samples.
For example, I take three random samples of students from a school and give the first sample a math test (sample size n1 = 50$n_1 = 50$), the second sample a reading test (n2 = 40$n_2 = 40$), and the third sample a physics test (n3 = 30$n_3 = 30$).
Let us say the students from the three samples are mutually exclusive. How can I calculate the confidence interval for the sum of mean scores, i.e., mean_math + mean_reading + mean_writing? Is there a command in Stata, SAS, or Matlab that I can use? Thanks.