Skip to main content

Point/interval estimation; CI for accident proportion

Short answer

Point estimation uses a single sample statistic (e.g., p̂ = 0.5775) to estimate the parameter. Interval estimation provides a range: p̂ ± z·SE. For n=400, 95% CI is (0.529, 0.626) for the true proportion of accidents partly due to unsafe conditions.

Explain the concept of (i) point estimation and (ii) Interval estimation of population properties. In a random sample of 400 industrial accidents, it was found that 231 were due to at least partially to unsafe working condition. 95% confidence intervals for the corresponding true proportion.

(i) Point estimation

A single value computed from the sample is used as the estimate of the unknown population parameter. The sample mean x̄ estimates μ, the sample proportion p̂ estimates P, and s² estimates σ². A good point estimator is unbiased, consistent, efficient and sufficient. It gives no idea of the error involved.

(ii) Interval estimation

An interval (L, U) is computed so that it contains the parameter with a stated probability, the confidence level (1 − α). It is based on the point estimate and its standard error: estimate ± (critical value) × (standard error). For a proportion, the interval is p̂ ± z·√(p̂q̂/n).

95% confidence interval for the true proportion

n = 400, x = 231
p̂ = 231/400 = 0.5775,  q̂ = 0.4225
SE = √(p̂q̂/n) = √(0.5775×0.4225/400) = 0.0247
margin = 1.960 × 0.0247 = 0.0484
limits = 0.5775 ± 0.0484 = (0.5291, 0.6259)

Answer: the 95% confidence interval for the true proportion of accidents partly due to unsafe working conditions is (0.529, 0.626), i.e. about 52.9% to 62.6%.

✓ Answer checked by Claude Sonnet 5.5

Related questions

All Probability and Statistics chapter 7 questions →