Confidence Intervals

Confidence interval is a range of values we can be certain (with high probability) that our true value lies in.

Example: Assume we have a dataset of 100 randomly chosen cricket bowlers, and their bowling speeds. Given the mean is 135 kmph and standard deviation is 12 kmph.

Calculate the 95% confidence interval

The confidence interval formula is given by,

$\bar{\mu} \pm z \cdot {\sigma \over \sqrt{n}}$

where, z = z-score, n = no. of samples

z-score for 95% confidence is 1.96 (i.e. from -1.96 to 1.96)

$135 \pm 1.96 \cdot {12 \over \sqrt{100}}$

$135 \pm 2.35$

Therefore, the 95% confidence interval is 132.65 to 137.35

The table for z-score of most common confidence intervals is given below.

Confidence	z-score
80%	1.282
85%	1.440
90%	1.645
95%	1.960
99%	2.576
99.5%	2.807
99.9%	3.291