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  2. Sample size determination - Wikipedia

    en.wikipedia.org/wiki/Sample_size_determination

    We might decide that we want a 95% confidence level, meaning we are 95% confident that the true average satisfaction level falls within the calculated range. We also decide on a margin of error, of ±3%, which indicates the acceptable range of difference between our sample estimate and the true population parameter.

  3. Confidence interval - Wikipedia

    en.wikipedia.org/wiki/Confidence_interval

    The confidence interval can be expressed in terms of a long-run frequency in repeated samples (or in resampling): "Were this procedure to be repeated on numerous samples, the proportion of calculated 95% confidence intervals that encompassed the true value of the population parameter would tend toward 95%." [19] The confidence interval can be ...

  4. Rule of three (statistics) - Wikipedia

    en.wikipedia.org/wiki/Rule_of_three_(statistics)

    A 95% confidence interval is sought for the probability p of an event occurring for any randomly selected single individual in a population, given that it has not been observed to occur in n Bernoulli trials. Denoting the number of events by X, we therefore wish to find the values of the parameter p of a binomial distribution that give Pr(X = 0 ...

  5. 68–95–99.7 rule - Wikipedia

    en.wikipedia.org/wiki/68–95–99.7_rule

    In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr or 3 σ, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean ...

  6. Binomial proportion confidence interval - Wikipedia

    en.wikipedia.org/wiki/Binomial_proportion...

    In contrast, it is worth noting that other confidence interval may have coverage levels that are lower than the nominal , i.e., the normal approximation (or "standard") interval, Wilson interval, [8] Agresti–Coull interval, [13] etc., with a nominal coverage of 95% may in fact cover less than 95%, [4] even for large sample sizes.

  7. Margin of error - Wikipedia

    en.wikipedia.org/wiki/Margin_of_error

    For a confidence level, there is a corresponding confidence interval about the mean , that is, the interval [, +] within which values of should fall with probability . Precise values of z γ {\displaystyle z_{\gamma }} are given by the quantile function of the normal distribution (which the 68–95–99.7 rule approximates).

  8. Prediction interval - Wikipedia

    en.wikipedia.org/wiki/Prediction_interval

    For example, to calculate the 95% prediction interval for a normal distribution with a mean (μ) of 5 and a standard deviation (σ) of 1, then z is approximately 2. Therefore, the lower limit of the prediction interval is approximately 5 ‒ (2⋅1) = 3, and the upper limit is approximately 5 + (2⋅1) = 7, thus giving a prediction interval of ...

  9. Confidence and prediction bands - Wikipedia

    en.wikipedia.org/wiki/Confidence_and_prediction...

    Each of these confidence intervals covers the corresponding true value f(x) with confidence 0.95. Taken together, these confidence intervals constitute a 95% pointwise confidence band for f(x). In mathematical terms, a pointwise confidence band ^ () with coverage probability 1 − α satisfies the following condition separately for each value of x: