Unexplained respiratory symptoms reported by athletes are often incorrectly considered secondary to exercise-induced asthma. The article "High Prevalence of Exercise-Induced Laryngeal Obstruction in Athletes" (Medicine and Science in Sports and Exercise, 2013: 2030-2035) suggested that many such cases could instead be explained by obstruction of the larynx. In a sample of 88 athletes referred for an asthma workup, 31 were found to have the EILO condition.
a. Calculate and interpret a confidence interval using a 95% confidence level for the true proportion of all athletes found to have the EILO condition under these circumstances.
b. What sample size is required if the desired width of the 95% CI is to be at most .04, irrespective of the sample results?
c. Does the upper limit of the interval in (a) specify a 95% upper confidence bound for the proportion being estimated? Explain.