Hypothesis testing, correlation and regression

Hypothesis testing asks whether sample evidence is strong enough to reject a claim about a population. The null hypothesis (H0) states no effect or no difference; the alternative (H1) states what the researcher suspects. The test computes a statistic from the sample and asks: if H0 were true, how unlikely is this result? Worked example: a machine fills packs at a claimed mean of 50 grams with standard deviation 8. A sample of 64 packs averages 52 grams. Standard error = 8 / 8 = 1, so z = (52 - 50) / 1 = 2. At the 5% level the critical value is 1.96, and 2 exceeds it — reject H0 and conclude the machine overfills. The logic is always the same: statistic, critical value, decision.