Linear regression: confidence interval of the average of 10 slopes, error of propagation and error of the mean

I have 10 regression slopes in one group, each slope has its associated standard error. Now I want to find the average slope of this group and the associated standard error which will be used to find the 95% confidence interval. I know the standard error of the mean is the sum of the squared deviation from the mean divided by the square root of the sample size and the sample size is 10 in this case. I can calculate the average slope and find the deviation of each slope by subtracting the mean. But since each slope has an associated standard error, how do I take into account of this when I calculate the standard error of the mean or actually I don’t need include the error from each slope?

For the confidence range of the average slope of this group, I am using 1.96*standard error of the mean.

Your help will be much appreciated!