One way to construct a 95% confidence interval for a population proportion p is to begin with the probability statement

and solve for p.

(a) Rewrite the probability statement by squaring all three terms inside the inequality above.

(b) Note that (-1.96)2 = (1.96)2, and therefore the expression inside the inequality statement can be expressed as a quadratic equation for the variable p. Write out this quadratic equation.

(c) Solve the quadratic equation for p. Based on this solution, write the expression for the Wilson confidence interval for p.

P(-1.9 p-p P-1.96 1.96 = 0.95, VP(1 - p)/n