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.