Intrabatch variabilty estimated from pooled SD and confidence intervals

#1
I would like to calculate intrabatch variability of parameter A, which is normally distributed.
I have data of 50 batches (the same process), for each batch I have one representative sample with sample size = 10. I have calculated pooled SD from the samples of all 50 batches (I assume this is legit, since all the batches have the same sources of variability and pooled SD should be more accurate estimator than just one sample with sample size 10 should be). Then I would like to calculate two sided confidence interval for parameter A for one batch with the formula below:

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Where A is the mean of the parameter of the batch in question (calculated from one sample), t is t value, α is significance level of two sided confidence interval, n is degrees of freedom for t value, Spooled is pooled standard deviation and m is sample size.

My question is:
What values should be used for n and m in that case? The problem is we have different sample sizes for SD and mean of A.
  1. Should the sample size used for calculation of pooled SD be used:
    • n = 50 * 10 - 50 = 450
    • m = 50 * 10 = 500
  2. Should the sample size of individual batch (used for caluclation of mean A) be used:
    • n = 10 - 1
    • m = 10
  3. Should any combination of point 1 and 2 be used?
Any rationale would be highly appreciated.

Thank you in advance