The random variable X X\,X has the distribution X∼B(26,0.40)X \sim B(26, 0.40)X∼B(26,0.40) under the null hypothesis H0H_0H0: p=0.40p = 0.40p=0.40, and the alternative hypothesis is H1H_1H1: p≠0.40p \ne 0.40p=0.40, where p p\,p is the population proportion of successes.
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%.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.