Question

The mean area µ of the several thousand apartments in a new development is advertised to be 1250 square feet. A tenant group thinks that the apartments are smaller than advertised. They hire an engineer to measure a sample of apartments to test their suspicion. The appropriate null and alternative hypotheses, H0 and Ha, for this test are

Answer 1

The appropriate null hypothesis is
`H_0: \mu = 1250`

The appropriate alternate hypothesis is
`H_a: \mu < 1250`

Explanation:

At the null hypothesis, we test if the mean area is the advertised area of 1250 square feet, that is:

`H_0: \mu = 1250`

A tenant group thinks that the apartments are smaller than advertised.

Smaller, thus, at the alternate hypothesis, we test if the mean area is less than the advertised area of 1250 square feet, that is:

`H_a: \mu < 1250`