Question

Determine whether carpeted rooms have more bacteria than uncarpeted rooms at the level of significance. Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers.

Carpeted Un-Carpeted
15.9 8.1 15 7.2 10.4 6.1
11.2 16 11.2 6.8 11.3 6.8
8.6 10 12.1 6.3

Requried:
State the null and alternative hypotheses. Let population 1 be carpeted rooms and population 2 be uncarpeted rooms.

Answer 1

The null (H
`_(0)`) and alternative (H
`_(1)`) hypotheses can be stated as follows:

H
`_(0)`: μ
`_(1)` = μ
`_(2)`.

H
`_(1)`: μ
`_(1)` > μ
`_(2)`.

Explanation:

In the question, the given assertion is that carpeted rooms have more bacteria than uncarpeted rooms, i.e. μ
`_(1)` > μ
`_(2)`.

The assertion made in the question can either be the null hypothesis (H
`_(0)`) or the alternate hypothesis (H
`_(1)`). An equality must be present in the null hypothesis. The alternative hypothesis expresses the exact opposite of the null hypothesis if the claim is the null hypothesis.

Therefore, the null (H
`_(0)`) and alternative (H
`_(1)`) hypotheses can be stated as follows:

H
`_(0)`: μ
`_(1)` = μ
`_(2)`.

H
`_(1)`: μ
`_(1)` > μ
`_(2)`.