In a major industry where well over 100,000 manufacturing employees are represented by a single union, a simple random sampling of n 100 union members finds that 57% of those in the sample intend to vote for the new labor contract negotiated by union and management representatives.
a. What is the 99% confidence interval for π = the population proportion of union-represented employees who intend to vote for the labor contract?
b. Based on your response to part (a), does contract approval by the union appear to be a "sure thing"? Why or why not?