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# Statistical Inference

Statistical inference is the application of statistical methods to a set of data in order to infer conclusions about the data sample drawn from a population. Use Wolfram|Alpha's powerful algorithmic know-how to compute the validity of hypotheses, the sample size required to draw valid conclusions and the confidence intervals for various inferred population statistics.

Sample Size Determination

Compute the sample size necessary to draw statistically valid conclusions about a population from a dataset.

Find the sample size needed to estimate a binomial parameter:

Find the sample size needed to estimate a population mean:

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Confidence Intervals

Compute the confidence intervals for population statistics based on sample size or the characteristics of the data sample.

Compute a confidence interval for a binomial parameter:

Find a confidence interval for the difference between binomial parameters:

Compute a confidence interval for a population mean:

Find a confidence interval for the difference between population means:

Find a confidence interval for the standard deviation of a normal population:

Find a confidence interval for the variance of a normal population:

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Hypothesis Testing

Test the validity of hypotheses and conjectures regarding statistical quantities derived from a sample of data.

Test for a binomial parameter:

Test for the difference between binomial parameters:

Test for a population mean:

Test for the difference between population means:

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