Suppose that after 6 months of a new form of treatment for chronic schizophrenia, 18 patients exhibited some improvement, 4 did not change, and 6 patients actually got worse.

a. Using the sign test, can you reject the null hypothesis (that the new treatment has no effect) at the .05 level? (Show the z score and p value that you used to answer this question.)

b. A more conservative way to conduct the binomial test is to assign half of the tied cases arbitrarily to each category (one pair is discarded if there is an odd number of ties). Redo part (a) after applying this approach to tied cases.