It is well known that a placebo, a fake medication or treatment,can sometimes have a positive effect just because patients oftenexpect the medication or treatment to be helpful. An article gaveexamples of a less familiar phenomenon, the tendency for patientsinformed of possible side effects to actually experience those sideeffects. The article cited a study in which a group of patientsdiagnosed with benign prostatic hyperplasia is randomly dividedinto two subgroups. One subgroup of size 55 received a compound ofproven efficacy along with counseling that a potential side effectof the treatment is erectile dysfunction. The other subgroup ofsize 52 is given the same treatment without counseling. Thepercentage of the no-counseling subgroup that reported one or moresexual side effects is 19.23%, whereas 41.82% of the counselingsubgroup reported at least one sexual side effect. State and testthe appropriate hypotheses at significance level 0.05 to decidewhether the nocebo effect is operating here. [Note: Theestimated expected number of "successes" in the no-counselingsample is a bit shy of 10, but not by enough to be of great concern(some sources use a less conservative cutoff of 5 rather than10).]
State the relevant hypotheses. (Use p1 forthe true proportion of patients experiencing one or more sexualside effects when given no counseling and p2for the true proportion of patients experiencing one or more sexualside effects when receiving counseling that a potential side effectof the treatment is erectile dysfunction.)
Calculate the test statistic and P-value. (Round yourtest statistic to two decimal places and your P-value tofour decimal places.)
z= -2.54
p-value=?
