Question

. A cardiothoracic surgeon is interested to see if her hospital has a greater survival rate than the national average. A 2014 report by the Organ Procurement and Transplantation Network and the Scientific Registry of Transplant Recipients states that the overall survival rate after a heart transplant in the U.S. is about 88 percent after 1 year. At her hospital in the past 20 years there were 110 heart transplant recipients 90 of which survived one year after.

(a)(4) Which are the appropriate hypotheses to test? i. H0 : µ = 90 vs. Ha : µ 6= 90 ii. H0 : π = .88 vs. Ha : π > .88 iii. H0 : π = .83 vs. Ha : π 6= .83 iv. H0 : π = .88 vs. Ha : π 6= .88

(b)(4) Are the technical conditions satisfied? Explain.

(c)(4) Assuming that the technical conditions are satisfied, calculate the test statistic.

(d)(4) Calculate the p-value.

(e)(4) Draw a conclusion based on the p-value in the context of the problem at the .05 significance level.

Answer 1

(a)   ii. H0 : π = .88 vs. Ha : π > .88

(b) n*p = 110*0.88 = 96.8 10

n*(1 - p) = 110*(1 - 0.88) = 13.2 10

Yes, the technical conidtion is met.

(c) The test statistic, z = (90/110 - 0.88)/0.88*0.12/110 = -2.00

(d) The p-value is 0.9770.

(e) Since the p-value (0.9770) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the hospital has a greater survival rate than the national average.