We guess, based on historical data, that 30% of graduating highschool seniors in a large city will have completed a firstyear calculus course. What’s the minimum sample size needed to construct a 95% confidence interval for a proportion with a margin of error of 2.5%?  

Your mathematics instructor claims that, over the years, 88% of his students have said that math is their favorite subject. In this year’s class, however, only 21 out of 32 students named math as their favorite class. The instructor decides to construct a confidence interval for the true population proportion based on the sample value. What’s the correct value for the standard error of SE in this case?  
