Scenario: When shirts are made, there can occasionally be defects (such as improper stitching). But too many such defective shirts can be a sign of substandard manufacturing.

Suppose, in the past, your favorite department store has had only one defective shirt per 200 shirts (a prior defective rate of only .005). But you suspect that the store has recently switched to a substandard manufacturer. So you decide to test to see if their overall proportion of defective shirts today is higher.

Suppose that, in a random sample of 200 shirts from the store, you find that 27 of them are defective, for a sample proportion of defective shirts of .135. You want to test whether this is evidence that the store is "guilty" of substandard manufacturing, compared to their prior rate of defective shirts.

The null hypothesis in this case is:

The alternative hypothesis in this case is: