Question

In a study of 798 randomly selected medical malpractice​ lawsuits, it was found that 476 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 correct hypothesis to be tested? What is the test​ statistic? ​(Round to two decimal places as​ needed.) What is the​ P-value? What is the conclusion about the null​ hypothesis? What is the final​ conclusion?

Answer 1

Solution:

Given:

Sample Size = n = 798

x = Number of  medical malpractice ​lawsuits were dropped or dismissed = 476

Thus sample proportion of medical malpractice lawsuits are dropped or dismissed is:

Significance level = 0.01

Claim: most medical malpractice lawsuits are dropped or dismissed

That is: p > 0.5

Part a) What is the correct hypothesis to be tested?

H0: p = 0.5

Vs

H1: p > 0.5

Part b) What is the test​ statistic?

Part c) What is the​ P-value?

P-value = P( Z > z test statistic )

P-value = P( Z > 5.45 )

P-value = 1 - P( Z< 5.45)

Since z = 5.45 is outside the range of z values, we need to use Excel to find P-value.

=1-NORM.S.DIST(z , cumulative)

=1-NORM.S.DIST(5.45,TRUE)

= 0.000000025

=0.0000

Thus

P-value = 0.0000

Or we can use TI 84 calculator:

Steps:

Press STAT and select TESTS

Select 1-prop z test

Enter numbers:

Click on Calculate and press Enter

z = 5.45

P-value = 2.5026805E-8

P-value = 0.000000025

P-value = 0.0000

Part d) What is the conclusion about the null​ hypothesis?

Since P-value = 0.0000 < 0.01 significance level, we reject null hypothesis.

Part e) What is the final ​conclusion?

Since we have rejected null hypothesis , there is sufficient evidence to support claim that most medical malpractice lawsuits are dropped or dismissed.