Question

In a study of 789 randomly selected medical malpractice​ lawsuits, it was found that 520 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.

Answer 1

In this case, we will use the z-test fro proportions to do the hypothesis testing of the number of the lawsuits being dropped or dismissed.  

Null Hypothesis(H_o): Most medical malpractice lawsuits are dropped or dismissed. In this case, we define most as 80% of the cases are dropped or dismissed. Therefore, p=0.8

Alternate Hypothesis(H₁): Most medical malpractice lawsuits are not dropped or dismissed. Therefore, p 0.8.

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.

Here, the sample proportion, p_o = 0.82 = 589/720 as per the claim.

We need to now calculate the sample standard deviation, = , where n = 789.

The value of   is 0.0137.

Now, we find out the value of the z-statistic, which is given as z= p-p_o/ .

z= -1.46.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than -1.46 or greater than 1.46.Now, using the significance level, i.e = 0.01, we find out the p-value. You can find the values using the z-table(Please google a z-table).

P(z < -1.46) = 0.0721, and P(z > 1.46) = 0.0721. Therefore, p-value is 0.14, which is greater than 0.05. Hence, we fail to reject the null hypothesis. There is no sufficient evidence to state that 80% of the lawsuits are dropped or dismissed.

Now, you can also conduct a similar test for a different percentage assumption. For example, you can assume the "Most" means 90% or 95%. Just follow the same steps as above.