95% confidence interval for p

(0.3767, 0.4633)

Large counts check: successes = 210, failures = 290 (both at least 10, condition met).

Steps

  1. 1.p-hat = x / n = 210 / 500 = 0.42
  2. 2.z* for 95% confidence = 1.96
  3. 3.SE = sqrt(p-hat(1 - p-hat) / n) = sqrt(0.42 x 0.58 / 500) = 0.02207
  4. 4.margin of error = 1.96 x 0.02207 = 0.0433
  5. 5.interval = 0.42 ± 0.0433 = (0.3767, 0.4633)

Confidence interval calculator (mean and proportion) · free from StatsLearn