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Suppose the proportion of students in School A diagnosed with ADHD is [tex]p_1[/tex] and the proportion of students in School B diagnosed with ADHD is [tex]p_2[/tex]. State the null hypothesis for a test to determine if School A has the lower proportion of students diagnosed with ADHD.

Select the correct answer below:
A. [tex]H_0: p_1 - p_2 = 0[/tex]
B. [tex]H_0: p_1 - p_2 \ \textgreater \ 0[/tex]
C. [tex]H_0: p_1 - p_2 \ \textless \ 0[/tex]
D. [tex]H_0: p_1 - p_2 \neq 0[/tex]

Sagot :

GinnyAnsweridn
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]
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