91影视

Out of 1228 randomly selected medical malpractice lawsuits, 856 of them were dropped or dismissed.

The null hypothesis is written as follows:

The proportion of medical malpractice lawsuits subjects who were dropped or dismissedequals50%.

\({H_0}:p = 0.5\)

The alternative hypothesis is written as follows:

The proportion of medical malpractice lawsuits subjects dropped or dismissed is more than 50%.

\({H_1}:p > 0.5\)

The test is right-tailed.

The sample sizeequalsn=1228.

The sample proportion of medical malpractice lawsuits subjects dropped or dismissed isas follows:

\[\begin{array}{c}\hat p = \frac{{856}}{{1228}}\\ = 0.697\end{array}\]

The population proportion of medical malpractice lawsuits subjects dropped or dismissed is equal to 0.5.

The value of the test statistic is computed below:

\(\begin{array}{c}z = \frac{{\hat p - p}}{{\sqrt {\frac{{pq}}{n}} }}\\ = \frac{{0.697 - 0.5}}{{\sqrt {\frac{{0.5\left( {1 - 0.5} \right)}}{{1228}}} }}\\ = 13.807\end{array}\)

Thus, z=13.807.

Referring to the standard normal distribution table, the critical value of z at\(\alpha = 0.01\)for a right-tailed test equals2.3263.

Referring to the standard normal distribution table, the p-value for the test statistic value of 13.807 equals0.000.

Since the p-value is less than 0.05, the null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of medical malpractice lawsuits subjects dropped or dismissed is greater than 0.5.

Since most malpractice lawsuits are either dropped or dismissed, it should be comforting for the physicians as they can be relieved without any trial.