Math  /  Data & Statistics

QuestionIn a study of 789 randomly selected medical malpractice lawsuits, it was found that 484 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.
Which of the following is the hypothesis test to be conducted? A. H0:p=0.5\mathrm{H}_{0}: \mathrm{p}=0.5 B. H0:p>0.5H_{0}: p>0.5 H1:p0.5H_{1}: p \neq 0.5 H1:p=0.5H_{1}: p=0.5 C. H0:p0.5H_{0}: p \neq 0.5 D. H0:p<0.5H_{0}: p<0.5 H1:p=0.5H_{1}: p=0.5 H1:p=0.5H_{1}: p=0.5 E. H0:p=0.5H_{0}: p=0.5 F. H0:p=0.5\mathrm{H}_{0}: \mathrm{p}=0.5 H1:p>0.5H_{1}: p>0.5 H1:p<0.5H_{1}: p<0.5
What is the test statistic? z=6.37z=6.37 (Round to two decimal places as needed.) What is the P -value? P -value == \square (Round to three decimal places as needed.)

Studdy Solution

STEP 1

1. We are testing the claim that most medical malpractice lawsuits are dropped or dismissed.
2. "Most" implies a proportion greater than 0.5.
3. We will use a significance level of 0.05.

STEP 2

1. Formulate the null and alternative hypotheses.
2. Calculate the test statistic.
3. Determine the P-value.
4. Make a decision based on the P-value and significance level.

STEP 3

Formulate the null and alternative hypotheses.
- Null hypothesis (H0H_0): p=0.5 p = 0.5 - Alternative hypothesis (H1H_1): p>0.5 p > 0.5
The correct hypothesis test to be conducted is:
F. H0:p=0.5 H_0: p = 0.5 , H1:p>0.5 H_1: p > 0.5

STEP 4

Calculate the test statistic.
Given: - Sample size (nn) = 789 - Number of successes (xx) = 484 - Sample proportion (p^\hat{p}) = 484789\frac{484}{789}
Calculate the test statistic using the formula:
z=p^p0p0(1p0)n z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}
Where p0=0.5p_0 = 0.5.
p^=4847890.613 \hat{p} = \frac{484}{789} \approx 0.613
z=0.6130.50.5×0.5789 z = \frac{0.613 - 0.5}{\sqrt{\frac{0.5 \times 0.5}{789}}}
z6.37 z \approx 6.37

STEP 5

Determine the P-value.
Since this is a right-tailed test, we look for the probability that z z is greater than 6.37.
Using standard normal distribution tables or a calculator, find:
P(Z>6.37) P(Z > 6.37)
The P-value is very small, typically less than 0.001.

STEP 6

Make a decision based on the P-value and significance level.
Since the P-value is less than the significance level of 0.05, we reject the null hypothesis.
Conclusion: There is sufficient evidence to support the claim that most medical malpractice lawsuits are dropped or dismissed.
The P-value is approximately:
0.000 \boxed{0.000}

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