I have a sample of data with n=200 and I would like to predict my descriptive statistics such as mean, Std Dev and 95% CI when I have specific sample size for example n=10 based on the current study. I assumed my population follows the Normal distribution and I applied t test to calculate CI. What I have done, I applied random sampling with replacement with n=10 from the original sample and repeated the process 100 times and calculated the mean of each 100 samples then calculate the mean(100 means), sd(100 means) then 95%CI(100 means) to get a good prediction of descriptive statistics for any random sample with size n=10. I was wondering if this approach is correct or not? Or the other solution could be to get the mean(100 means) and Pooled.Sd(100 sd) then calculate 95%CI. Could you please give me advise?
Thanks in advance for your help.