Question

2.The mean area of several thousand apartments in a new development is advertised to be 1,100 square feet. A consumer advocate has received numerous complaints that the apartments are smaller than advertised. A state building inspector is sent out to measure a sample of apartments. State the null and the alternative hypothesis to test this claim.

Answer 1

Null Hypothesis,
`H_0` :
`\mu` = 1,100 square feet

Alternate Hypothesis,
`H_A` :
`\mu` < 1,100 square feet

Explanation:

We are given that the mean area of several thousand apartments in a new development is advertised to be 1,100 square feet.

A consumer advocate has received numerous complaints that the apartments are smaller than advertised.

Let
`\mu` = mean area of several apartments.

So, Null Hypothesis,
`H_0` :
`\mu` = 1,100 square feet

Alternate Hypothesis,
`H_A` :
`\mu` < 1,100 square feet

Here, null hypothesis states that the mean area of apartments are same as advertised.

On the other hand, alternate hypothesis states that the mean area of apartments are smaller than advertised.

So, this would be the appropriate null and the alternative hypothesis to test this claim.