Question

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 55 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 52 is given the same treatment without counseling. The percentage of the no-counseling subgroup that reported one or more sexual side effects is 15.38%, whereas 45.45% 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 p₁ 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.)

H₀: p₁ − p₂ = 0
H_a: p₁ − p₂ > 0

H₀: p₁ − p₂ = 0
H_a: p₁ − p₂ ≠ 0   

H₀: p₁ − p₂ = 0
H_a: p₁ − p₂ ≥ 0

H₀: p₁ − p₂ = 0
H_a: p₁ − 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.)

z =

P-value =

State the conclusion in the problem context.

Reject H₀. There is sufficient evidence to suggest that a higher proportion of men will experience one or more sexual side effects if told that a potential side effect of the BHP treatment is erectile dysfunction than if they weren't told of this potential side effect.

Fail to reject H₀. There is insufficient evidence to suggest that a higher proportion of men will experience one or more sexual side effects if told that a potential side effect of the BHP treatment is erectile dysfunction than if they weren't told of this potential side effect.    

Reject H₀. There is insufficient evidence to suggest that a higher proportion of men will experience one or more sexual side effects if told that a potential side effect of the BHP treatment is erectile dysfunction than if they weren't told of this potential side effect.

Fail to reject H₀. There is sufficient evidence to suggest that a higher proportion of men will experience one or more sexual side effects if told that a potential side effect of the BHP treatment is erectile dysfunction than if they weren't told of this potential side effect.

Answer 1

Here we have given that,

Claim: To check whether the nocebo effect is operating or not.

The Hypotheses is

Ho: P1= P2

v/s

Ha: P1 > P2

we have given that,

n1= one subgroup size =55

p1=percentage of the no counseling subgroup= 45.45 %

=1^st sample proportion = 0.4545

n2=second subgroup size =55=52

p2=percentage of the counseling subgroup=15.38 %

=2^st sample proportion = 0.1538

= level of significance= 0.05

Now, we can find the test statistics

=   

=3.59

Now, we want to find the P-value

Pvalue = P( Z> 3.59) (as this is right tailed test)

              = (1- P (Z < 3.59))

              = ( 1- 0.9998 )) using P(Z< 3.59) calculated using excel = NORMSDIST(3.59)

              =0.0002

Decision:

Here P value < 0.05

we reject the Ho null hypothesis

Conclusion:

There is sufficient evidence to suggest that a higher proportion of men will experience one or more sexual side effects if told that a potential side effect of the BHP treatment is erectile dysfunction than if they weren't told of this potential side effect.