An article in the British Medical Journal [“Comparison of Treatment of Renal Calculi by Operative Surgery, Percutaneous Nephrolithotomy, and Extracorporeal Shock Wave Lithotripsy” (1986, Vol. 292, pp. 879–882)] reported that percutaneous nephrolithotomy (PN) had a success rate in removing kidney stones of 289 out of 350 (83%) patients. However, when the stone diameter was considered, the results looked different. For stones of <2cm, 87% (234/270) of cases were successful. For stones of ≥2cm, a success rate of 69% (55/80) was observed for PN.

(a) Are the successes and size of stones independent? Use α = 0.05.

(b) Find the P-value for this test.