It is known that 20% of online purchases require manual review. A manager believes that this proportion has increased since a change to the checkout system.
A random sample of 55 purchases made since the change is taken, and 17 require manual review.
Stating your hypotheses clearly, test the manager's belief at the 2.5% significance level.
State, with a reason, the conclusion you would have reached at the 5% significance level.
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.