O: Statistical hypothesis testing: Understand and apply the language of statistical hypothesis testing, developed through a binomial model: null hypothesis, alternative hypothesis, significance level, test statistic, 1-tail test, 2-tail test, critical value, critical region, acceptance region, p -value; extend to correlation coefficients as measures of how close data points lie to a straight line and be able to interpret a given correlation coefficient using a given p -value or critical value (calculation of correlation coefficients is excluded).

The idea

You must use hypothesis testing language correctly. For a binomial test, define H0 (the default hypothesis) and H1 (the alternative), choose a significance level, calculate the test statistic (number of successes), and compare with critical values or p-value. Hypothesis tests assess evidence against H0, not test H1. Know 1-tail vs 2-tail, critical region, acceptance region. For correlation, interpret a given r using a given p-value or critical value: if p < significance level, reject H0. For a two-tailed test, reject H0 if |r| > critical value; for a one-tailed test, compare the signed r with a direction-specific critical value. You do not calculate r.

For example: Testing a coin for bias: H0: p=0.5, H1: p>0.5, n=20, X~B(20,0.5), find critical region for 5% one-tail.

What earns the marks

• Define null and alternative hypotheses in context, using correct symbols.
• State the significance level and whether the test is 1-tail or 2-tail.
• Identify the test statistic and its distribution under H0.
• Find critical value(s) and critical region, and state acceptance region.
• Calculate or use p-value to make a decision, comparing with significance level.

Common mistakes and how to put them right

• Confusing 1-tail and 2-tail tests.

  Put it right by reading the alternative hypothesis direction.

• Misinterpreting p-value as probability H0 is true.

  Put it right by stating it is probability of observed or more extreme given H0.

• For correlation, thinking r close to 1 means causation.

  Put it right by explaining it measures linear association only.

• Applying |r| > critical value to a one-tailed correlation test.

  Put it right by using the signed r and a direction-specific critical value.

Exam tips

• Always write hypotheses in terms of the population parameter, not sample statistic.
• For binomial, state X~B(n,p) under H0 and use tables or calculation for critical region.
• For correlation, compare given p-value with significance level or given r with critical value, and conclude in context; check whether the test is one- or two-tailed before using |r|.