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Answer :
Let's approach the task of expressing the null and alternative hypotheses for the given situation.
1. Understanding the Problem:
- We have historical data indicating that the mean weight of male counselors is 186 pounds.
- New research suggests that the mean is now at most 186 pounds.
2. Identifying the Hypotheses:
- The null hypothesis ([tex]\(H_0\)[/tex]) is usually a statement of no effect or no difference. It is what we assume to be true unless we have evidence to suggest otherwise. In this case, the null hypothesis states that the mean weight, [tex]\(\mu\)[/tex], is equal to the historical weight.
- The alternative hypothesis ([tex]\(H_1\)[/tex]) is what you want to prove. It's usually based on the research claim. Here, the claim is that the mean weight is at most 186 pounds, meaning it could be equal to or less than 186 pounds.
3. Setting Up the Hypotheses:
- Null Hypothesis ([tex]\(H_0\)[/tex]): The mean weight is 186 pounds. In symbolic form, this is expressed as [tex]\(\mu = 186\)[/tex].
- Alternative Hypothesis ([tex]\(H_1\)[/tex]): The mean weight is at most 186 pounds, which means [tex]\(\mu \leq 186\)[/tex].
These hypotheses can now be expressed in symbolic form as:
- [tex]\(H_0: \mu = 186\)[/tex]
- [tex]\(H_1: \mu \leq 186\)[/tex]
In summary, for this statistical testing scenario, the null hypothesis assumes no change from the historical mean, while the alternative hypothesis reflects the new research claim.
1. Understanding the Problem:
- We have historical data indicating that the mean weight of male counselors is 186 pounds.
- New research suggests that the mean is now at most 186 pounds.
2. Identifying the Hypotheses:
- The null hypothesis ([tex]\(H_0\)[/tex]) is usually a statement of no effect or no difference. It is what we assume to be true unless we have evidence to suggest otherwise. In this case, the null hypothesis states that the mean weight, [tex]\(\mu\)[/tex], is equal to the historical weight.
- The alternative hypothesis ([tex]\(H_1\)[/tex]) is what you want to prove. It's usually based on the research claim. Here, the claim is that the mean weight is at most 186 pounds, meaning it could be equal to or less than 186 pounds.
3. Setting Up the Hypotheses:
- Null Hypothesis ([tex]\(H_0\)[/tex]): The mean weight is 186 pounds. In symbolic form, this is expressed as [tex]\(\mu = 186\)[/tex].
- Alternative Hypothesis ([tex]\(H_1\)[/tex]): The mean weight is at most 186 pounds, which means [tex]\(\mu \leq 186\)[/tex].
These hypotheses can now be expressed in symbolic form as:
- [tex]\(H_0: \mu = 186\)[/tex]
- [tex]\(H_1: \mu \leq 186\)[/tex]
In summary, for this statistical testing scenario, the null hypothesis assumes no change from the historical mean, while the alternative hypothesis reflects the new research claim.
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