Which of the following is an appropriate null hypothesis?
[tex]$H_o: \mu_o=\mu_a$[/tex]
[tex]$H_0: \mu_0 \neq \mu_a$[/tex]
[tex]$H_0: \mu_0\ \textgreater \ \mu_a$[/tex]
[tex]$H_0: \mu_0\ \textgreater \ \mu_a$[/tex]
Answer (1)
The null hypothesis states there is no effect or difference.
The null hypothesis includes an equality sign.
The appropriate null hypothesis from the given options is: H o : μ o = μ a .
Explanation
Understanding the Null Hypothesis The null hypothesis, denoted as H 0 , is a statement that there is no effect or no difference. It is a statement that we are trying to disprove. The null hypothesis always includes an equality sign.
Analyzing the Options The given options are:
H o : μ o = μ a
H 0 : μ 0 = μ a
\mu_a"> H 0 : μ 0 > μ a
\mu_a"> H 0 : μ 0 > μ a
Only the first option, H o : μ o = μ a , includes an equality sign. The other options use inequality signs ( = and "> > ), which are used for alternative hypotheses.
Conclusion Therefore, the appropriate null hypothesis is H o : μ o = μ a .
Examples
In medical research, the null hypothesis might state that a new drug has no effect on patients compared to a placebo. In manufacturing, it could state that there is no difference in the quality of products produced by two different machines. The null hypothesis provides a baseline against which to compare the results of an experiment or study. For example, if we want to test if the average height of students in two different schools is the same, we would set up the null hypothesis as H 0 : μ 1 = μ 2 , where μ 1 and μ 2 are the average heights of students in the two schools, respectively.
