It is estimated that 780,000 surgical site infections (SSIs) occur each year.SSIs are the second most common type of healthcare-associated infections in U.S.hospitals and account for an extra $3.5 to $10 billion in healthcare costs per year.The national SSIs rate is 1.9%.A Georgetown medical office was interested in determining if their SSI rate were smaller than the national average.Out of a sample of 277 patients in their study,only one infection occurred.Is the Georgetown medical office SSIs rate less than the national average SSIs rate? (Note: Use a significance level of .05. )

A) Yes,because the P-value is less than .05
B) Yes,because the P-value is greater than .05
C) No,because the P-value is less than .05
D) No,because the P-value is greater than .05

Question

Britney Cababat · Accepted Answer

Final Answer : A, Explanation :  We can use a one-sample proportion test to test whether the Georgetown medical office SSI rate is less than the national average SSI rate of 1.9%.Let p be the proportion of patients in the Georgetown medical office sample who had SSIs.Null hypothesis: H0: p = 0.019Alternative hypothesis: Ha: p < 0.019Under the null hypothesis, we use the normal approximation to the binomial distribution to calculate the probability of observing one or fewer SSIs in a sample of 277 patients:P(X <= 1) = P(X = 0) + P(X = 1) = binom.cdf(1, 277, 0.019)where binom.cdf is the cumulative distribution function for the binomial distribution.Using a calculator or software, we find:P(X <= 1) = 0.003This is the p-value of the test, which is the probability of observing one or fewer SSIs in a sample of 277 patients assuming the null hypothesis is true.Since the significance level is 0.05, we reject the null hypothesis if the p-value is less than 0.05.Since the p-value is less than 0.05, we reject the null hypothesis and conclude that there is evidence that the Georgetown medical office SSI rate is less than the national average SSI rate at the 0.05 significance level. Therefore, the best choice is A.

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