Each year, the Florida Department of Education grades K–12 schools on a scale of A to F. In spring 2009, 71 schools in Duval changed their grade compared to the previous year, 46 improving, and 25 declining. In the nearby county of Putnam, which is much more rural, 9 schools changed their grade, 6 improving and 3 declining.

(a) Can Duval state that their observed proportion of improving schools differs significantly from what would be expected if improving and declining were equally likely events? (Use α = 0.05).

(b) Can Putnam make the same statement? Hint: This data set is not large enough for the z approximation. You can calculate a p value using the binomial distribution. LO.1