Probability & Statistics 2 · Hypothesis testing
Understand the nature of a hypothesis test, including one-tailed and two-tailed tests, null hypothesis, alternative hypothesis, significance level, critical region, acceptance region, and test statistic.
Formulate hypotheses and carry out a hypothesis test for a single observation from a binomial distribution using direct probability evaluation.
Formulate hypotheses and carry out a hypothesis test for a single observation from a binomial distribution using a normal approximation.
Interpret outcomes of hypothesis testing in context.
Understand the terms Type I error and Type II error in relation to hypothesis testing.
Calculate the probabilities of making Type I and Type II errors in specific situations involving tests based on a normal distribution or direct evaluation of binomial probabilities.
Confusing the null hypothesis with what the researcher wants to prove; H0 is the statement of no effect or no difference.
Incorrectly choosing between a one-tailed and two-tailed test; the choice depends on whether the claim specifies a direction (increase/decrease) or just a difference.
Forgetting to apply continuity correction when approximating a binomial distribution with a normal distribution.
Interpreting 'accept H0' as proving H0 is true, rather than 'there is insufficient evidence to reject H0'.
Confusing Type I and Type II errors, or their probabilities (significance level vs. beta).
Not stating conclusions in context or implying certainty (e.g., 'the claim is proven') rather than using phrases like 'there is sufficient evidence to suggest...'.