I have 1000 values from which I calculate the mean A and the standard deviation std A and the 95% confidence interval. I have another 1000 values from which I calculate the mean B and the standard deviation std B and the 95% confidence interval.
If I now calculate the mean of A and B, is it valid to calculate the mean of std A and std B (i.e. the means of the standard devaitions) and the mean of the two confidence intervals?