A manufacturer knows that 12% of its light bulbs fail within a year. A new production method is introduced, and the manufacturer wants to know whether the proportion failing within a year has changed.
A random sample of 200 bulbs made by the new method is taken, and X X\,X is the number that fail within a year.
State suitable null and alternative hypotheses for the manufacturer's test.
State the distribution of X X\,X under the null hypothesis.
State whether this test is one-tailed or two-tailed, and give a reason.
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.