A college admissions officer sampled 120 entering freshmen and found that 42 of them scored more than 550 on the math SAT.

a. Find a point estimate for the proportion of all entering freshmen at this college who scored more than 550 on the math SAT.

b. Construct a 98% confidence interval for the proportion of all entering freshmen at this college who scored more than 550 on the math SAT.

c. According to the College Board, 39% of all students who took the math SAT in 2009 scored more than 550.

The admissions officer believes that the proportion at her university is also 39%. Does the confidence interval contradict this belief? Explain.