It is known that the proportion of components from a supplier that meet a specification is 0.42. A manufacturer believes this proportion has increased, and tests a random sample of 35 components at the 5% significance level. The random variable X X\,X is the number in the sample that meet the specification.
Find the least value of X X\,X for which the null hypothesis would be rejected.
Find the actual significance level of a test based on this critical region.
In the sample, 22 components meet the specification. State the conclusion of the test in context.
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.