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.