A scientist is investigating whether a new computer-aided scoring system for x-rays does a better job of identifying cancerous tumors than current practice. The scientist has x-rays from 200 known cancer cases and 200 known controls. Using the new test, 175 of the cases and 44 of the controls test positive. a) (6 pts) Calculate a 95% confidence interval for the sensitivity of the new test. b) (6 pts) Calculate a 90% confidence interval for the specificity of the new test. c) (1 pts) Would a 95% confidence interval for the specificity to be wider or narrower than the 90% interval