Estimation & Hypothesis Testing

Inference & Testing

Estimation Methods

Method of Moments (MOM): Equate sample moments to population moments.
Maximum Likelihood (MLE): Find parameters that maximize the probability of the observed data.

Confidence Intervals

Instead of a point estimate, we provide a range of plausible values.

$\sigma$ known: z-interval
$\sigma$ unknown: t-interval

Hypothesis Testing

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The Process

Null Hypothesis ( $H_0$ ): The default position (e.g., “no effect”).
P-value: Probability of seeing data this extreme if $H_0$ is true.
Decision: Reject $H_0$ if P-value $< \alpha$ (significance level).

Common tests include z-test, t-test, $\chi^2$ -test, and F-test.