Statistical inference is the process of drawing conclusions about a population from sample data, primarily through hypothesis testing involving the null hypothesis (H₀, assuming no effect or difference) and alternative hypothesis (H₁, indicating an effect or difference), while accounting for Type I (false positive, probability α like 0.05) and Type II (false negative, probability β) errors. Common methods include the t-test for comparing means with unknown population standard deviation or small samples, z-test for large samples or known standard deviation, and chi-square test for categorical data to assess goodness-of-fit or independence. Decisions rely on comparing the p-value (probability of observing data as extreme assuming H₀ true) to the significance level α: reject H₀ if p ≤ α (evidence for H₁), otherwise fail to reject, enabling evidence-based generalizations under uncertainty.

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