How do I construct and interpret confidence intervals for CFA Level I?

This is one of the most commonly misunderstood concepts in statistics — even among professionals. Let's get it right.

Construction Formula:

Confidence Interval = Point Estimate ± (Critical Value x Standard Error)

For a population mean:

CI = x-bar ± z(α/2) x (σ / √n)

Common Critical Values:

Worked Example:

An analyst at Silverstone Advisors samples 49 stocks and finds the average P/E ratio is 18.5 with a population standard deviation of 7.0.

95% confidence interval:

• Standard error = 7.0 / √49 = 1.0
• CI = 18.5 ± 1.96 x 1.0 = 18.5 ± 1.96
• CI = (16.54, 20.46)

Correct Interpretation:

If we repeated this sampling process many times, 95% of the resulting intervals would contain the true population mean P/E ratio.

INCORRECT Interpretation (common mistake):

"There is a 95% probability that the true mean is between 16.54 and 20.46." -- This is wrong because the true mean is a fixed number, not random. It's either in the interval or not.

When to use z vs. t:

Factors that narrow the interval:

1. Larger sample size (reduces standard error)
2. Lower confidence level (smaller critical value)
3. Lower population variability (smaller σ)

Exam tip: The CFA exam will test both construction and interpretation. Don't say "95% probability the mean is in the interval" — say "95% of similarly constructed intervals would contain the true mean." This distinction is explicitly tested.

Practice confidence interval problems in our CFA Level I question bank.