Question

In a study of 806 randomly selected medical malpracticeâ lawsuits, it was found that 513 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 hypothesis test to beâ conducted?

Answer 1

Solution :

$H_0: p = 0.5$

$H_a: p > 0.5$

Alpha, α = 0.01

The sample proportion is :

$p'=\frac{x}{n}$

   $=\frac{513}{806}$

   = 0.636

Test statistics, $z=\frac{p'-p}{\sqrt{\frac{pq}{n}}}$

$z=\frac{0.636-0.5}{\sqrt{\frac{0.5\times 0.5}{806}}}$

$z=\frac{0.136}{0.0176}$

z = 7.727

The p value = 0.00001

Here we observe that p value is less than α, and so we reject the hypothesis $H_0$.

Therefore, there is sufficient evidence,