How to Compute 95 Confidence Interval?

Determine the sample statistic, such as the sample mean or sample proportion

Choose the confidence level, 95%

Find the critical value

Use z = 1.96 for a large sample or known population standard deviation

Use the t value with n – 1 degrees of freedom for a small sample with unknown population standard deviation

Compute the standard error

For a mean with known population standard deviation: SE = σ / √n

For a mean with unknown population standard deviation: SE = s / √n

For a proportion: SE = √[p̂(1 – p̂) / n]

Compute the margin of error

Margin of error = critical value × standard error

Compute the confidence interval

Lower bound = sample statistic – margin of error

Upper bound = sample statistic + margin of error

Write the interval as

sample statistic ± margin of error

or [lower bound, upper bound]