As superintendent of Chicago schools, you are interested in seeing whether ACT scores have improved between 1993 and 1994. You obtain a sample of 56 schools and find that scores have improved in 19 and worsened in 37.

(a) How can you tell if your observed results are plausible if there has been no change in ACT scores?

(b) From the binomial test, you find that the observed significance level is 0.0231. Does this support the claim that ACT scores have improved?

(c) Explain to the mayor whether it's possible that ACT scores have not really changed?

(d) What's the probability that you would see results as extreme as the ones observed when average ACT scores have not changed?