Out of 100 psychiatric patients given a new form of treatment, 60 improved, while 40 got worse.

a. Use a chi-square test to decide whether you can reject the null hypothesis that the treatment is totally ineffective (i.e., that patients are equally likely to improve or get worse).

b. Redo the significance test in part (a) using the z score formula (i.e., normal approximation) for the binomial test. Explain the relationship between the z score you calculated in this part and the χ2 value you calculated in part (a).