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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

Respuesta :

Answer:

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

Step-by-step explanation:

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

[tex]H_0:p= 0.5\\\\H_a: p>0.5[/tex]

The sample mean is:

[tex]\hat p=X/n=496/810=0.612[/tex]

The standard deviation is estimated as:

[tex]\sigma_p=\sqrt{p(1-p)/n}=\sqrt{0.5*0.5/810}=\sqrt{0.000308642}\\\\\sigma_p=0.017[/tex]

The statistic is calculated as:

[tex]z=\frac{\hat p-p-0.5/n}{\sigma_p}=\frac{0.612-0.500-0.000}{0.017}=\frac{0.112}{0.017} =6.59[/tex]

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.

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