An article in the British Medical Journal [“Comparison of Treatment of Renal Calculi by Operative Surgery, Percutaneous Nephrolithotomy, and Extra-Corporeal Shock Wave Lithotrips” (1986, Vol. 292, pp. 879–882)] repeated that percutaneous nephrolithotomy (PN) had a success rate in removing kidney stones of 289 of 350 patients. The traditional method was 78% effective.

(a) Is there evidence that the success rate for PN is greater than the historical success rate? Find the P-value.

(b) Explain how the question in part (a) could be answered with a confidence interval.