A health study involves 1000 randomly selected deaths, with 273 of them caused by heart disease (based on data from Statistics Canada).
a. Using the sample data, construct a 99% confidence interval for the proportion of all deaths caused by heart disease.
b. Use the sample data as a pilot study and find the sample size necessary to estimate the proportion of all deaths caused by heart disease. Assume that you want 98% confidence that the estimate is in error by no more than 0.01.