The random variable X X\,X has the distribution X∼B(24,0.35)X \sim B(24, 0.35)X∼B(24,0.35) under the null hypothesis H0H_0H0: p=0.35p = 0.35p=0.35, and the alternative hypothesis is H1H_1H1: p≠0.35p \ne 0.35p=0.35.
A two-tailed test is to be carried out at the 5% significance level, with a probability of at most 0.025 in each tail.
Find the critical region for this test.
Find the actual significance level of a test based on this critical region.
Explain why the actual significance level is not equal to 5%.
162 exam-style questions on AQA A Level Maths 2.5 O: Statistical hypothesis testing, covering 2.5.1 Language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, and 2.5.3 Hypothesis test for a Normal mean (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.