Exercise 1: A 95% Confidence Interval for n=16 — Possible Solution ==================================================================== GIVEN ------------------------------ n = 16, sample mean = 550, sigma = 48 STEP 1: THE STANDARD ERROR ------------------------------ SE = sigma / sqrt(n) = 48 / sqrt(16) = 48 / 4 = 12 STEP 2: THE 95% CONFIDENCE INTERVAL ------------------------------ Per this chapter's own formula, using z* = 1.96 for 95% confidence: margin = z* x SE = 1.96 x 12 = 23.52 CI = 550 +/- 23.52 = [526.48, 573.52] WHY THIS WORKS AS AN ANSWER ------------------------------ The standard error is computed first using Chapter 2's own formula, and the confidence interval is built directly on top of it using this chapter's own point-estimate +/- (critical value x SE) formula with the correct 95% critical value.