Question

Stat crunch In a study of 810810 randomly selected medical malpractice​ lawsuits, it was found that 496496 of them were dropped or dismissed. Use a 0.010.01 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed.

Which of the following is the hypothesis test to be? conducted?

A. Upper H 0 : p less than 0.5
Upper H 1 : p equals 0.5

B. Upper H 0 : p greater than 0.5
Upper H 1 : p equals 0.5

C. Upper H 0 : p equals 0.5
Upper H 1 : p not equals 0.5

D. Upper H 0 : p equals 0.5
Upper H 1 : p less than 0.5

E. Upper H 0 : p not equals 0.5
Upper H 1 : p equals 0.5

F. Upper H 0 : p equals 0.5
Upper H 1 : p greater than 0.5

Answer 1

a) There is enough evidence that most medical malpractice lawsuits are dropped or dismissed.

b) F. Upper H 0 : p equals 0.5

Upper H 1 : p greater than 0.5

Explanation:

If the claim is that most (more than half) medical malpractice lawsuits are dropped or dismissed, the null and alternative hypothesis are:

`H_0:p= 0.5\\\\H_a: p>0.5`

The sample mean is:

`\hat p=X/n=496/810=0.612`

The standard deviation is estimated as:

`\sigma_p=√(p(1-p)/n)=√(0.5*0.5/810)=√(0.000308642)\\\\\sigma_p=0.017`

The statistic is calculated as:

`z=(\hat p-p-0.5/n)/(\sigma_p)=(0.612-0.500-0.000)/(0.017)=(0.112)/(0.017) =6.59`

The P-value of this statistic is P=0.000, so the effect is significant.

The null hypothesis is rejected.

There is enough evidence that most medical malpractice lawsuits are dropped or dismissed.