# Combining two estimates

The number of participants in a particular sport in the USA in 2014 was estimated by a research group at 3,000,000. This estimate came with a standard error. The number of hospitalizations associated with that sport in 2014 was estimated by another research group at 15,000 and this estimate came with a coefficient of variation. I wish to combine these estimates and to estimate the likely number of hospitalizations per 100,000 participants, with a 95% CI. How do I go about this?

You are asking about pooled means and variances. As far as I understand, the data you have is two means $m_1$, $m_2$ and two sample sizes $n_1$, $n_2$. Variances $s_1^2$ and $s_2^2$ can be easily obtained from standard errors ($\mathrm{SE} = s_i / \sqrt{n_i}$) and coefficient of variation ($\mathrm{CV} = s_i / m_i$) since you have all the needed information. Having all this information you can obtain pooled mean from $k$ sources
$$m_p = \frac{\sum_{i=1}^k n_i m_i}{\sum_{i=1}^k n_i}$$
$$s_p^2 = \frac{ \sum_{i=1}^k (n_i - 1) s_i^2 }{ \sum_{i=1}^k (n_i - 1) }$$