Significance tests for proportions

Learning objectives

Identify a one-sample z-test as the procedure for a claim about a population proportion, define the parameter in context, and state the null and alternative hypotheses with a one-sided or two-sided alternative taken from the investigative question

Check the conditions for a one-sample z-test for a proportion: a random sample, the 10% condition, and np₀ and n(1 − p₀) both at least 10, using the null value p₀ rather than the sample proportion

Calculate the test statistic z = (p̂ − p₀) ÷ √(p₀(1 − p₀)/n) and the p-value, and interpret the p-value as the probability, when the null hypothesis is true, of a result at least as extreme as the one observed

Compare the p-value with the significance level α, decide whether to reject the null hypothesis, and state the conclusion in context without claiming that either hypothesis has been proved

Describe a Type I error and a Type II error and their consequences in context, state that the probability of a Type I error equals α, and explain how the sample size, the significance level, the standard error and the distance of the true value from the null value affect the power of a test

Carry out a two-sample z-test for a difference between two population proportions: hypotheses, conditions, the pooled proportion, the test statistic, the p-value and a conclusion in context