Question

In a study of

820820

randomly selected medical malpractice​ lawsuits, it was found that

492492

of them were dropped or dismissed. Use a

0.050.05

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 not equals 0.5H0: p≠0.5

Upper H 1 : p equals 0.5H1: p=0.5

B.

Upper H 0 : p less than 0.5H0: p<0.5

Upper H 1 : p equals 0.5H1: p=0.5

C.

Upper H 0 : p equals 0.5H0: p=0.5

Upper H 1 : p greater than 0.5H1: p>0.5

D.

Upper H 0 : p equals 0.5H0: p=0.5

Upper H 1 : p less than 0.5H1: p<0.5

E.

Upper H 0 : p greater than 0.5H0: p>0.5

Upper H 1 : p equals 0.5H1: p=0.5

F.

Upper H 0 : p equals 0.5H0: p=0.5

Upper H 1 : p not equals 0.5H1: p≠0.5

What is the test​ statistic?

zequals=nothing

​(Round to two decimal places as​ needed.)

What is the​ P-value?

​P-valueequals=nothing

​(Round to three decimal places as​ needed.)

What is the conclusion about the null​ hypothesis?

A.

RejectReject

the null hypothesis because the​ P-value is

less than or equal toless than or equal to

the significance​ level,

alphaα.

B.

Fail to rejectFail to reject

the null hypothesis because the​ P-value is

less than or equal toless than or equal to

the significance​ level,

alphaα.

C.

RejectReject

the null hypothesis because the​ P-value is

greater thangreater than

the significance​ level,

alphaα.

D.

Fail to rejectFail to reject

the null hypothesis because the​ P-value is

greater thangreater than

the significance​ level,

alphaα.

What is the final​ conclusion?

A.There

is notis not

sufficient evidence to support the claim that most medical malpractice lawsuits are dropped or dismissed.

B.There

isis

sufficient evidence to support the claim that most medical malpractice lawsuits are dropped or dismissed.

C.There

isis

sufficient evidence to warrant rejection of the claim that most medical malpractice lawsuits are dropped or dismissed.

D.There

is notis not

sufficient evidence to warrant rejection of the claim that most medical malpractice lawsuits are dropped or dismissed.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.5

H_a : p 0.5

n = 820

x = 492

= x / n = 492 / 820 = 0.6

P₀ = 0.5

1 - P₀ = 1 - 0.5 = 0.5

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.6 - 0.5 / [(0.5 * 0.5) / 820]

= 2.308 = 2.31

Test statistic = 2.31

P(z > 2.31) = 1 - P(z < 2.31) = 1 - 0.9896 = 0.0104

P-value = 2 * 0.0104 = 0.0208

= 0.05

P-value <

Reject the null hypothesis .

A.

Reject the null hypothesis because the​ P-value is less than or equal the significance​ level, alpha α.

C)

There is sufficient evidence to warrant rejection of the claim that most medical malpractice lawsuits are dropped or dismissed.