4)

4. (12 ptS.) A study examined the effectiveness of Botox injections in the corrugator supercilii muscles for the treatment of chronic migraines. Of the 30 migraine-prone patients participating in the study, 19 reported complete migraine elimination. (a) Determine a plus four 95% condence interval for the population proportion of migraine patients with complete migraine remission following such Botox injections. 0}) How large a sample :1 would you need to estimate p with margin of error 0.04 with 95% condence? Use 31" = 0.63 as an estimated value for p. (c) How large a sample :1 would you need to estimate p with margin of error 0.04 with 95% condence? Use f; = 0.50 as the estimated value for p