Answer :
To answer the question about the conclusion of the hypothesis test, let's break down and understand the problem step-by-step.
1. Understand the Hypotheses:
- We have two hypotheses:
- Null Hypothesis ([tex]\(H_0\)[/tex]): [tex]\(\mu = 196\)[/tex]. This means the average weight of men is 196 pounds, the same as in 2010.
- Alternative Hypothesis ([tex]\(H_1\)[/tex]): [tex]\(\mu > 196\)[/tex]. This suggests that the average weight of men has increased since 2010.
2. Conclusion Based on Hypothesis Testing:
- If you fail to reject the null hypothesis ([tex]\(H_0\)[/tex]), it means that the data does not provide strong enough evidence to support the claim that the average weight of men has increased.
- In statistical terms, failing to reject the null hypothesis implies that there isn't sufficient evidence to believe there is a change from the known condition (in this case, 196 pounds).
3. Formulate the Conclusion:
- Since the scenario in question states that we fail to reject the null hypothesis, the appropriate conclusion is:
- "There is not sufficient evidence to warrant rejection of the null hypothesis that the average weight of men is the same."
This conclusion suggests that the available data, whatever it might be, does not convincingly show an increase in average weight from 2010.
1. Understand the Hypotheses:
- We have two hypotheses:
- Null Hypothesis ([tex]\(H_0\)[/tex]): [tex]\(\mu = 196\)[/tex]. This means the average weight of men is 196 pounds, the same as in 2010.
- Alternative Hypothesis ([tex]\(H_1\)[/tex]): [tex]\(\mu > 196\)[/tex]. This suggests that the average weight of men has increased since 2010.
2. Conclusion Based on Hypothesis Testing:
- If you fail to reject the null hypothesis ([tex]\(H_0\)[/tex]), it means that the data does not provide strong enough evidence to support the claim that the average weight of men has increased.
- In statistical terms, failing to reject the null hypothesis implies that there isn't sufficient evidence to believe there is a change from the known condition (in this case, 196 pounds).
3. Formulate the Conclusion:
- Since the scenario in question states that we fail to reject the null hypothesis, the appropriate conclusion is:
- "There is not sufficient evidence to warrant rejection of the null hypothesis that the average weight of men is the same."
This conclusion suggests that the available data, whatever it might be, does not convincingly show an increase in average weight from 2010.
