#!/usr/bin/env python
# coding: utf-8

# In[1]:


import numpy as np


# In[3]:


treat = 330.8
treat_se = 99.7

placebo = 188.1
placebo_se = 55.5

n = 15


# Formula for SE of difference:
# 
# $$SE = \sqrt{\frac{SD_T^2}{n_T} + \frac{SD_C^2}{n_C}}$$
# 
# and $SE = SD/\sqrt{n}$, so for this example:
# 
# $$SE = \sqrt{SE_T^2 + SE_C^2}$$

# In[6]:


SE_diff = np.sqrt(99.7**2 + 55.5**2)
SE_diff


# Hence, a 95% confidence interval for the difference would be:

# In[7]:


d = treat-placebo
d - 2*SE_diff, d + 2*SE_diff


# Which, given n=15 and the variability, is pretty unccertain.