Answer :
To determine the null hypothesis for the situation described, we first need to understand the basic concept of hypothesis testing. The null hypothesis, denoted as [tex]\( H_0 \)[/tex], is a statement that there is no effect or no difference, and it is assumed true until evidence suggests otherwise. It usually represents the status quo or the commonly accepted fact.
In this scenario, the commonly accepted fact is that there are only 76 known Javan Rhinos left in the world. Steve Wilson, however, believes that this report is false and suggests there are more than 76 Javan Rhinos. Therefore, we have to formulate the null hypothesis as the opposite of what Steve Wilson proposes.
Here are the options provided:
a) [tex]\( H_0: n \geq 76 \)[/tex]
b) [tex]\( H_0: n \leq 76 \)[/tex]
c) [tex]\( H_0: n < 76 \)[/tex]
d) [tex]\( H_0: n > 76 \)[/tex]
Since Steve believes there are more than 76 Javan Rhinos, he is suggesting [tex]\( n > 76 \)[/tex]. Thus, the null hypothesis, being the opposite of this, should state that there are 76 or fewer Javan Rhinos. This would translate to:
[tex]\( H_0: n \leq 76 \)[/tex]
Therefore, the correct null hypothesis that matches this intention is option b) [tex]\( H_0: n \leq 76 \)[/tex].
In this scenario, the commonly accepted fact is that there are only 76 known Javan Rhinos left in the world. Steve Wilson, however, believes that this report is false and suggests there are more than 76 Javan Rhinos. Therefore, we have to formulate the null hypothesis as the opposite of what Steve Wilson proposes.
Here are the options provided:
a) [tex]\( H_0: n \geq 76 \)[/tex]
b) [tex]\( H_0: n \leq 76 \)[/tex]
c) [tex]\( H_0: n < 76 \)[/tex]
d) [tex]\( H_0: n > 76 \)[/tex]
Since Steve believes there are more than 76 Javan Rhinos, he is suggesting [tex]\( n > 76 \)[/tex]. Thus, the null hypothesis, being the opposite of this, should state that there are 76 or fewer Javan Rhinos. This would translate to:
[tex]\( H_0: n \leq 76 \)[/tex]
Therefore, the correct null hypothesis that matches this intention is option b) [tex]\( H_0: n \leq 76 \)[/tex].
