The mean height of a certain kind of plant is 185 centimeters. Suppose we want to carry out a hypothesis test to see if the mean height when these plants are treated with a certain chemical differs from 185. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test.
H0: mean = 185
H1: mean ≠ 185
To determine the null hypothesis (H0) and the alternative hypothesis (H1) for the hypothesis test, we need to consider what we are trying to determine or evaluate.
In this case, we want to test if the mean height of plants treated with a certain chemical differs from 185 centimeters. We can assume that the population mean height without the chemical treatment is also 185 centimeters.
The null hypothesis (H0) states that there is no significant difference between the mean height of plants treated with the chemical and 185 centimeters. Mathematically, it can be written as:
H0: μ = 185
On the other hand, the alternative hypothesis (H1) contradicts the null hypothesis and suggests that there is a difference between the mean height of the treated plants and 185 centimeters. There are three possibilities for the alternative hypothesis:
1. One-tailed alternative hypothesis (greater than): If we only want to test if the mean height of treated plants is greater than 185 centimeters, we write:
H1: μ > 185
2. One-tailed alternative hypothesis (less than): If we want to test if the mean height of treated plants is less than 185 centimeters, we write:
H1: μ < 185
3. Two-tailed alternative hypothesis: If we want to test if the mean height of treated plants differs from 185 centimeters without specifying the direction, we write:
H1: μ ≠ 185
The selection of the appropriate alternative hypothesis depends on the research question and the expected direction of the difference.