## Confidence interval on an average

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nil has a statistical package available for getting statistical distributions. This is useful for computing confidence intervals using the student-t tables. Here is an example of computing a 95% confidence interval on an average.

import numpy as np
from scipy.stats.distributions import  t

n = 10 # number of measurements
dof = n - 1 # degrees of freedom
avg_x = 16.1 # average measurement
std_x = 0.01 # standard deviation of measurements

# Find 95% prediction interval for next measurement

alpha = 1.0 - 0.95

pred_interval = t.ppf(1-alpha/2.0, dof) * std_x / np.sqrt(n)

s = ['We are 95% confident the next measurement',
' will be between {0:1.3f} and {1:1.3f}']
print ''.join(s).format(avg_x - pred_interval, avg_x + pred_interval)

We are 95% confident the next measurement will be between 16.093 and 16.107