Subject: Mathematics
Book: Maths Mastery
Confidence intervals estimate a population parameter (e.g., mean) from a sample, providing a range in which the parameter likely lies. A basic approach for a large sample is Mean ± z*(σ/√n), where z is the z-score for the desired confidence level (like z=1.96 for ~95%), σ is the population standard deviation (or sample-based estimate), and n is the sample size. For instance, if a sample mean is 100 with σ=15 and n=100, a 95% CI is 100 ± 1.96*(15/10)=100 ± 2.94 → (97.06, 102.94). Confidence intervals are vital in research, polling, and risk management, ensuring informed conclusions with quantifiable uncertainties.
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