📄 Cheat Sheets — Probability & Statistics 2

Key facts, formulas and common mistakes for 1 of 1 chapters

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6 key facts·5 common mistakes·10 definitions·5 exam tips

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Definitions

null hypothesis: In a hypothesis test, the claim is called the null hypothesis, abbreviated to H0.
alternative hypothesis: If you are not going to accept the null hypothesis, then you must have an alternative hypothesis to accept; the alternative hypothesis abbreviation is H1.
significance level: The percentage value of 5% is known as the significance level.
critical region: The range of values at which you reject the claim is the critical region or rejection region.
rejection region: The range of values at which you reject the claim is the critical region or rejection region.
acceptance region: The other region of the graph is the acceptance region.
test statistic: The test statistic is the calculated probability using sample data in a hypothesis test.
critical value: The value at which you change from accepting to rejecting the claim is the critical value.
Type I error: A Type I error occurs when a true null hypothesis is rejected.
Type II error: A Type II error occurs when a false null hypothesis is accepted.

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A hypothesis test evaluates a claim (null hypothesis, H0) against an alternative (H1) using sample data.Ch 01
The significance level (e.g., 5%) defines the probability of rejecting a true null hypothesis (Type I error).Ch 01
The critical region is the range of test statistic values for which H0 is rejected; its boundary is the critical value.Ch 01
Hypothesis tests for binomial distributions can use direct probability evaluation or a normal approximation (with continuity correction).Ch 01
A Type I error is rejecting a true H0, while a Type II error is accepting a false H0.Ch 01
One-tailed tests are used when H1 specifies a direction (e.g., p < 0.5), while two-tailed tests are for any difference (e.g., p ≠ 0.5).Ch 01

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✗Don't confuse the null hypothesis (H0) with what the researcher wants to prove; H0 is the statement of no effect or no difference.Ch 01
✗Remember to apply continuity correction when using a normal approximation to the binomial distribution.Ch 01
✗Don't interpret 'accept H0' as proving H0 is true; it means 'there is insufficient evidence to reject H0'.Ch 01
✗Don't confuse Type I and Type II errors, or their probabilities (significance level vs. beta).Ch 01
✗Don't incorrectly choose between a one-tailed and two-tailed test; the choice depends on the direction specified in the claim.Ch 01

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→Always state your null (H0) and alternative (H1) hypotheses clearly in terms of the population parameter (e.g., p).Ch 01
→Ensure your conclusion is stated in context, avoiding definitive language like 'proven' and instead using phrases like 'there is sufficient evidence to suggest...'.Ch 01
→Clearly show your working for calculating probabilities, especially for binomial distributions or normal approximations.Ch 01
→When using a normal approximation, explicitly state the distribution used (e.g., X ~ N(np, npq)) and show the continuity correction.Ch 01
→For two-tailed tests, remember to split the significance level equally between the two tails when determining critical regions or p-values.Ch 01