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...

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?