Calculating overall confidence intervals from two geometric means

[help12]

Hello,

I have the following data:

Group 1: Mean = 8985, confidence intervals = 5705–14150
67 people

Group 2: Mean = 7622, confidence intervals = 5486–10591
132 people

I do not have any individual data that made these means. Only the above data.

Overall mean: 8056.

Overall mean has been calculated as follows:

67*log(8985)+132*log(7622)
1789.8427

1789.8427/199
8.9941844

exp(8.9941844)
8056.0964

I need to calculate the overall CIs.

Is it the same method?

So for example the lower overall CI calculated as:

67*log(5705)+132*log(5486)
1716.0036

1716.0036/199
8.6231337

exp(8.6231337)
5558.7787

Or is this incorrect?

Thanks