To determine if School A has a lower proportion of students diagnosed with ADHD compared to School B, we need to set up a hypothesis test. Specifically, we are looking at the difference between the proportions [tex]$p_1$[/tex] (proportion of students diagnosed with ADHD in School A) and [tex]$p_2$[/tex] (proportion of students diagnosed with ADHD in School B).
The null hypothesis, denoted as [tex]$H_0$[/tex], is a statement we wish to test and is typically a statement of no effect or no difference.
Given the context of our test, where we are trying to determine if there is a difference in proportions between the two schools, the null hypothesis should state that there is no difference between the proportions of students diagnosed with ADHD in School A and School B. This translates to the following mathematical statement:
[tex]$
H_0: p_1 - p_2 = 0
$[/tex]
This hypothesis states that the proportion of students diagnosed with ADHD in School A is equal to the proportion in School B. This forms the basis against which we will test our alternative hypothesis, which would state that [tex]$p_1$[/tex] is different from or less than [tex]$p_2$[/tex].
Therefore, the correct answer is:
[tex]$
H_0: p_1 - p_2 = 0
$[/tex]
