Question

Suppose the legal counsel for a health care company claims claims that the majority of medical malpractice lawsuits were dropped or dismissed. Express in symbolic form the null and alternative hypotheses needed to test the legal counsel's claim. Define a "success" as occurring when a medical malpractice lawsuit is dropped or dismissed.

H₀ : p = 0.5
H_A : p > 0.5

H₀ : p < 0.5
H_A : p = 0.5

H₀ : p = 0.5
H_A : p < 0.5

H₀ : p ≠ 0.5
H_A : p = 0.5

H₀ : p = 0.5
H_A : p ≠ 0.5

H₀ : p > 0.5
H_A : p = 0.5

For the hypothesis test in Question 1, suppose that of 806 randomly selected medical malpractice lawsuits, 470 were either dropped or dismissed. Calculate the resulting p-value. Round your answer to three decimal places; add trailing zeros as needed.

The p-value = [MalPValue].

Answer 1

Solution :

Given that,

= 0.5

1 - = 0.5

n =806

x = 470

Point estimate = sample proportion = = x / n = 0.583

This a two- tailed test.

The null and alternative hypothesis is,

Ho: p = 0.5

Ha: p 0.5

Test statistics

z = ( - ) / *(1-) / n

= ( 0.583 - 0.5) / (0.5*0.5) / 806

= 4.72

P-value = 2 * P(Z > z )

= 2 * ( 1 - P(Z < 4.72 ))

= 2 * 0

= 0.000