It is known that 36% of the cars tested at a testing station fail on their first test. A new inspection procedure is introduced, and the manager believes that the proportion failing on the first test has decreased.
A random sample of 45 cars tested under the new procedure is taken, and X X\,X is the number that fail on the first test. A test is to be carried out at the 5% significance level.
State suitable null and alternative hypotheses.
Find the critical region for this test.
Find the actual significance level of a test based on this critical region.
In the sample, 9 cars fail on the first test. State the conclusion of the test in context.
40 exam-style questions on WJEC A Level Maths 2.5 Statistical hypothesis testing, covering 2.5.1 Statistical hypothesis testing, 2.5.2 Statistical hypothesis testing, 2.5.3 Statistical hypothesis testing, 2.5.4 Statistical hypothesis testing, and 2.5 Statistical hypothesis testing. Each one has a worked solution and a mark scheme showing where the marks go.