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Statistics for finance · level 2

Confidence intervals

Ninety-five percent means roughly two standard errors either side. Compute SE, double it, and you have the interval — 1.96 only matters when you are writing it down.

Theory: Risk Management

Worked example: Mean 50, σ = 20, n = 100. 95% margin of error?

SE2
z (95%)1.96
margin3.92
interval46.08 – 53.92

Step by step

  1. 1

    Standard error

    20 / √100 = 2

  2. 2

    95% uses 1.96 — call it 2

    2 × 2 ≈ 4

  3. 3

    Exact

    1.96 × 2 = 3.92

  4. 4

    The interval

    46.08 to 53.92

Mean 50, σ = 20, n = 100. 95% margin of error? = 3.92

The theory behind it

Intuition

A 95% interval is the estimate plus or minus about two standard errors — the '2' is the whole trick.

Common pitfalls

  • ×Saying there is a 95% chance the true value is in this interval.
  • ×Using 1.96 with a tiny sample where t is much larger.

In the interview

Sizing rounds where you must state a range, not a point.