Question
A hospital claims that at least 73% of their craniectomies are successful. A doctor of the hospital disputes this claim.
Identify the null hypothesis. (h_0 and h_a)
Identify the alternative hypothesis.
A hypothesis test is conducted at the 4% significance level. If the P-value is 0.047, what conclusion should be made?
A. The doctor cannot conclude that fewer than 73% of craniectomies are successful.
B. The doctor concludes that fewer than 73% of craniectomies are successful.
Identify the null hypothesis. (h_0 and h_a)
Identify the alternative hypothesis.
A hypothesis test is conducted at the 4% significance level. If the P-value is 0.047, what conclusion should be made?
A. The doctor cannot conclude that fewer than 73% of craniectomies are successful.
B. The doctor concludes that fewer than 73% of craniectomies are successful.
Answers
Answered by
GPT-4o mini
To identify the null and alternative hypotheses, we need to understand the claims being made.
1. **Null Hypothesis (H₀)**: This is the hypothesis that the hospital claims is true. In this case, it states that the proportion of successful craniectomies is at least 73%.
- \( H₀: p \geq 0.73 \)
2. **Alternative Hypothesis (H₁)**: This is the hypothesis that the doctor is disputing. It states that the proportion of successful craniectomies is less than 73%.
- \( H₁: p < 0.73 \)
### Summary of hypotheses:
- \( H₀: p \geq 0.73 \)
- \( H₁: p < 0.73 \)
Now, regarding the conclusion based on the P-value:
- The significance level (α) is 0.04.
- The P-value obtained from the test is 0.047.
Since the P-value (0.047) is greater than the significance level (0.04), we do not have enough evidence to reject the null hypothesis.
### Conclusion:
A. The doctor cannot conclude that fewer than 73% of craniectomies are successful.
1. **Null Hypothesis (H₀)**: This is the hypothesis that the hospital claims is true. In this case, it states that the proportion of successful craniectomies is at least 73%.
- \( H₀: p \geq 0.73 \)
2. **Alternative Hypothesis (H₁)**: This is the hypothesis that the doctor is disputing. It states that the proportion of successful craniectomies is less than 73%.
- \( H₁: p < 0.73 \)
### Summary of hypotheses:
- \( H₀: p \geq 0.73 \)
- \( H₁: p < 0.73 \)
Now, regarding the conclusion based on the P-value:
- The significance level (α) is 0.04.
- The P-value obtained from the test is 0.047.
Since the P-value (0.047) is greater than the significance level (0.04), we do not have enough evidence to reject the null hypothesis.
### Conclusion:
A. The doctor cannot conclude that fewer than 73% of craniectomies are successful.