Sampling and Hypothesis Tests Topic Review summary

Key learning points

• Null $H_0$ vs alternative $H_1$; one-tailed vs two-tailed.
• Test statistic under $H_0$; compare to critical region or use a $p$-value.
• Significance level $\\alpha$ is the Type I error probability.
• Conclusions in context: “sufficient/insufficient evidence…” — never claim absolute proof.
• Know the sampling distribution assumed (Normal / binomial / Poisson).

Worked example 1 — Tail

H_1:\\mu>\\mu_0 is which tail?

Working

Critical region in the upper end.

Worked example 2 — Context

Good conclusion style.

Working

Always relate to the claim.

Worked example 3 — Null H_0 vs alternative H_1; one-tailed vs

Null $H_0$ vs alternative $H_1$; one-tailed vs two-tailed.

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — Test statistic under H_0; compare to criti

Test statistic under $H_0$; compare to critical region or use a $p$-value.

Working

Attempt without notes, then check the answers PDF.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.