Intervalo de Confiança — Calculadora Online Grátis
Confidence interval for sample data with margin of error and statistical interpretation
The Confidence Interval Calculator constructs confidence intervals for a population mean or proportion from sample data, reporting the interval bounds, margin of error, and a plain-language interpretation. Select the confidence level (90%, 95%, or 99%) and enter your sample statistics. Researchers, data analysts, and statistics students use confidence intervals to communicate how precisely a sample represents a population.
Frequently Asked Questions
Sobre Esta Calculadora
A confidence interval provides a range of plausible values for an unknown population parameter based on sample data. A 95% confidence interval means that if you repeated the sampling procedure many times, approximately 95% of the resulting intervals would contain the true parameter. It does NOT mean there is a 95% probability that this specific interval contains the true value — a subtle but important distinction.
The interval is computed as: estimate ± (critical value × standard error). The critical value comes from the standard normal distribution (for large samples) or the t-distribution (for small samples). Wider intervals correspond to lower confidence, smaller samples, or higher data variability.
Confidence intervals are preferred over simple point estimates in research papers because they convey both the estimated value and its precision. Medical trials, public opinion polls, A/B testing, and quality control studies all report results using confidence intervals.
Tabela de amostra.
Exemplo Resolvido
95% confidence interval for mean exam score from a sample
Entradas:
- Sample mean (x̄): 74.2
- Sample standard deviation (s): 11.8
- Sample size (n): 40
- Confidence level: 95%
Passo a Passo:
- Standard error (SE) = s / √n = 11.8 / √40 = 11.8 / 6.324 = 1.866
- For 95% CI, use z* = 1.96 (large sample)
- Margin of error = z* × SE = 1.96 × 1.866 = 3.66
- Lower bound = 74.2 − 3.66 = 70.54
- Upper bound = 74.2 + 3.66 = 77.86