A hospital claims that at least 73% of their craniectomies are successful. A doctor of the hospital disputes this claim.

Question

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.

Answer 1

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.