According to a major financial reporting institution, the majority of companies reporting profits for the last quarter had beaten their estimates. A sample of 162 companies showed that 104 beat their estimates, 39 matched their estimates and 19 fell short of their estimates.
A) Calculate a 93% confidence interval for the proportion of companies that beat their estimates. How would you interpret this interval (in English)?
B) If the major institution wanted to estimate the proportion of all companies that fell short of their profit estimates for the last quarter within 2% with 96% confidence, how large of a sample should be taken?