When Conducting Research into the Efficacy of Drugs to Combat $\hat{p}$

Essay

When conducting research into the efficacy of drugs to combat psychologicaldisorders it is very common to use double blinding as a design strategy. In a doubleblind study neither the patient nor the doctor knows whether the patient is receivingthe treatment or the placebo drug. Does double blinding actually work?
That is, isthe doctor completely ignorant of the patient's assignment to their treatment group?
a) In a study involving the use of the drugs alprazolam and propranolol, 43 patientswith panic attack disorder and agoraphobia were treated. After completing thestudy the physicians involved were asked to guess the treatments. The physicianscorrectly guessed the treatments for 30 patients. Determine whether or not thesample size is large enough to use the standard normal distribution to find themargin of error. Be sure to show any supporting calculations.In a different study of double-blinding, the use of lithium as a treatment to counteractaggressive tendencies in adolescents was under study. In that study the physicianscorrectly guessed the treatment in 37 out of 57 patients.
b) Assuming these adolescents and doctors to be representative, estimate thepopulation proportion of patients for whom the doctor could correctly guess thetreatment.
c) If the physicians were simply guessing about the treatments administered to thepatients, p = 0.50 would be the proportion of correct guesses. If the physicianswere guessing, what would be the standard error of $\hat{p}$ ?
d) Based on the given data for the lithium treatment, calculate a 95% confidenceinterval for p, the proportion of correct guesses by physicians.
e) Suppose the researchers wished to get a more precise estimate of the proportion ofcorrect guesses of treatment when using lithium in this context. What samplesize would be needed to obtain a margin of error of 0.05 with 95% confidence?