In a study of 1228 randomly selected medical malpractice lawsuits, it was found

Question

In a study of 1228 randomly selected medical malpractice lawsuits, it was found that 856 of them were dropped or dismissed (based on data from the Physicians Insurers Association of America). Using a 0.01 significance level you want to test the claim that most medical malpractice lawsuits are dropped or dismissed. what is the null hypothesis? what is the alternate hypothesis? what is the significance level ? (10 pts) a- b- Is this a right-tailed, left-tailed, or two-tailed test? (8 pts) c- What is the sample test statistic? (8 pts) d- Draw a sketch showing the p-value area on the standard normal distribution. What is the p- value? (8 pts) e- Compare the level of significance and the p-value, what is your conclusion? (8 pts)

Explanation / Answer

a)
Null Hypothesis: H0: p = 0.5
Alternate hypothesis: H1: p > 0.5

Significance level = 0.01

b)
Right tailed test

c)
pcap = 856/1228 = 0.6971
SE = sqrt(0.5*0.5/1228) = 0.0143

Test statistics, z = (0.6971 - 0.5)/0.0143 = 13.7832

d)

p-value = 0.0000

e)

Reject the null hypothesis. There are sufficient evidence to conclude that the proportion of medical malpractice lawsuits dropped or dismissed is greater than 0.5

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