It is well known that a placebo, a fake medication or treatment, can sometimes have a positive effect just because patients often expect the medication or treatment to be helpful. An article gave examples of a less familiar phenomenon, the tendency for patients informed of possible side effects to actually experience those side effects. The article cited a study in which a group of patients diagnosed with benign prostatic hyperplasia is randomly divided into two subgroups. One subgroup of size 60 received a compound of proven efficacy along with counseling that a potential side effect of the treatment is erectile dysfunction. The other subgroup of size 50 is given the same treatment without counseling. The percentage of the no-counseling subgroup that reported one or more sexual side effects is 18%, whereas 45% of the counseling subgroup reported at least one sexual side effect. State and test the appropriate hypotheses at significance level 0.05 to decide whether the nocebo effect is operating here. [Note: The estimated expected number of "successes" in the no-counseling sample 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 than 10).] State the relevant hypotheses. (Use p, for the true proportion of patients experiencing one or more sexual side effects when given no counseling and p₂ for the true proportion of patients experiencing one or more sexual side effects when receiving counseling that a potential side effect of the treatment is erectile dysfunction.) Ho: P₁ Ha: P₁ Ho: P₁ Ha: P₁ O Ho: P₁ Ha: P₁ USE SALT Z = P₂ = 0 P₂ > 0 P-value = P₂ = 0 P₂ <0 Ho: P₁ P₂ = 0 Ha: P₁ P₂ 20 P₂ = 0 P₂ #0 Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) X X