Question

In a study of 775 randomly selected medical malpractice​lawsuits, it was found that 502 of them were dropped or dismissed. Use a 0.05 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed.

Answer 1

By using a 0.05 significance level, we can conclude that there is sufficient evidence that most medical malpractice lawsuits are dropped or dismissed.

How to test the claim for the medical malpractice lawsuits?

Since we have to compare whether the sample proportion is greater than or lesser than the population proportion, a one-tailed test would be used. Also, we would calculate the sample proportion of medical malpractice lawsuits that are dropped or dismissed as follows:

Sample proportion, p = x/n

Sample proportion, p = 502/775

Sample proportion, p = 0.6477

Mathematically, the null and alternative hypothesis is given by:

H₀: p = 0.5

H₁: p > 0.5

For the test statistic can be calculated by using this mathematical expression:

$z=\frac{\hat{p}\;-\;p_o}{\sqrt{\frac{p_o(1-p_o)}{n }} }$

Where:

• $\hat{p}$ represents the sample mean.
• $p_o$ represents the mean.
• n represents the number of subjects.

Substituting the given parameters into the formula, we have;

z = (0.6477 - 0.5)/√(0.5(1 - 0.5)/775)

z = 0.1477/√(0.25/775)

z = 0.1477/0.01796

z = 8.224.

For the p-value, we have:

p(z>8.224) = 0.0000

Therefore, the p-value (0.000) is less than the significance level α = 0.05. Based on this, we would reject the null hypothesis.

Read more on malpractice lawsuits here: brainly.com/question/13032617

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