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.