The article “Hospitals Dispute Medtronic Data on Wires” ( The Wall Street Journal, February 4, 2010) describes several studies of the failure rate of defibrillators used in the treatment of heart problems. In one study conducted by the Mayo Clinic, it was reported that failures within the first 2 years were experienced by 18 of 89 patients under 50 years old and 13 of 362 patients age 50 and older. Assume that these two samples are representative of patients who receive this type of defibrillator in the two age groups.
a. Construct and interpret a 95% confidence interval for the proportion of patients under 50 years old who experience a failure within the first 2 years.
b. Construct and interpret a 99% confidence interval for the proportion of patients age 50 and older who experience a failure within the first 2 years.
c. Suppose that the researchers wanted to estimate the pro-portion of patients under 50 years old who experience this type of failure with a margin of error of 0.03. How large a sample should be used? Use the given study results to obtain a preliminary estimate of the population proportion.