Module 5 · Inference · Topic 8

Null & Alternative Hypotheses

Null Hypothesis (H₀). The null hypothesis is the default claim of no effect or no difference. It always contains an equality (=, ≤, or ≥).

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Confidence Interval for a Mean: xbar +/- critical value * standard error - Estimate plus or minus a margin of error.
One-Sample Z Test: z = (xbar - mu_0) / (sigma / sqrt(n)) - Tests a sample mean against a null mean when population sigma is known.
Power: Power = 1 - beta - Probability of correctly rejecting a false null hypothesis.

P-value: The probability of results this extreme or more extreme, assuming the null hypothesis is true. Example: A p-value of 0.03 is evidence against H0 at alpha = 0.05.
Confidence Level: The long-run success rate of a confidence interval procedure. Example: A 95% method captures the true parameter in about 95% of repeated samples.
Type I Error: Rejecting the null hypothesis when it is actually true. Example: The significance level alpha is the Type I error rate.
Type II Error: Failing to reject the null hypothesis when the alternative hypothesis is true. Example: A false negative in a hypothesis test is a Type II error.
Power: The probability of rejecting the null hypothesis when it is false. Example: Power equals 1 - beta, where beta is the Type II error probability.

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