In a study of 784 randomly selected medical malpractice lawsuits, it was found that 510 of them were dropped or dismissed Use a 0.01 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed. What is the P-value? $P$-value $=0.00$ (Round to three decimal places as needed) What is the conclusion about the null hypothesis? A. Reject the null hypothesis because the P-value is greater than the significance level, $\alpha$ B. Reject the null hypothesis because the $P$-value is less than or equal to the significance level, $\alpha$ C Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, $\alpha$ D. Fail to reject the null hypothesis because the $P$-value is greater than the significance level, $\alpha$ What is the final conclusion? A. There is sufficient evidence to support the claim that most medical malpractice lawsuits are dropped or dismissed B. There is not sufficient evidence to warrant rejection of the claim that most medical malpractice lawsuits are dropped or dismissed. C. There is sufficient evidence to warrant rejection of the claim that most medical malpractice lawsuits are dropped or dismissed. D. There is not sufficient evidence to support the claim that most medical malpractice lawsuits are dropped or dismissed

Step 1 ：Define the null hypothesis as the proportion of medical malpractice lawsuits that are dropped or dismissed is 0.5, and the alternative hypothesis as the proportion is greater than 0.5.

Step 2 ：Use a one-sample z-test for a proportion to test this hypothesis.

Step 3 ：Calculate the test statistic as (p_hat - p_0) / sqrt((p_0 * (1 - p_0)) / n), where p_hat is the sample proportion, p_0 is the hypothesized population proportion, and n is the sample size.

Step 4 ：Calculate the P-value as the probability of observing a test statistic as extreme as the one calculated, under the null hypothesis.

Step 5 ：If the P-value is less than the significance level, reject the null hypothesis. If the P-value is greater than the significance level, fail to reject the null hypothesis.

Step 6 ：Given that n = 784, x = 510, p_0 = 0.5, calculate p_hat = x/n = 0.6505102040816326.

Step 7 ：Calculate the z-score as z = (p_hat - p_0) / sqrt((p_0 * (1 - p_0)) / n) = 8.428571428571427.

Step 8 ：Since the P-value is 0.0, which is less than the significance level of 0.01, reject the null hypothesis.

Step 9 ：Conclude that there is sufficient evidence to support the claim that most medical malpractice lawsuits are dropped or dismissed.

Step 10 ：The final answer is: The P-value is \(\boxed{0.000}\). We reject the null hypothesis because the P-value is less than or equal to the significance level, \(\alpha\). There is sufficient evidence to support the claim that most medical malpractice lawsuits are dropped or dismissed.