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

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### Investigating the Nocebo Effect in Benign Prostatic Hyperplasia Treatment

#### Introduction
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).

#### Formulation of Hypotheses
Use \( p_1 \) for the true proportion of patients experiencing one or more sexual side effects when given no counseling and \( p_2 \) 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. 

Select the appropriate hypotheses:
- \( H_0: \, p_1 - p_2 = 0 \)
- \( H_a: \, p_1 - p_2 < 0 \)

Visual representation of hypothesis options (with the correct option selected):

- \( \bigcirc \, H_0: \, p_1 - p_2 = 0 \quad H_a: \, p_1 - p_2 \geq 0 \)
- \( \bigodot \, H_0: \, p_1 - p_2 = 0 \quad H_a: \, p_1 - p_2 < 0 \) (Selected)
- \( \bigcirc \, H_0: \, p_1 - p_2 =
Transcribed Image Text:### Investigating the Nocebo Effect in Benign Prostatic Hyperplasia Treatment #### Introduction 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). #### Formulation of Hypotheses Use \( p_1 \) for the true proportion of patients experiencing one or more sexual side effects when given no counseling and \( p_2 \) 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. Select the appropriate hypotheses: - \( H_0: \, p_1 - p_2 = 0 \) - \( H_a: \, p_1 - p_2 < 0 \) Visual representation of hypothesis options (with the correct option selected): - \( \bigcirc \, H_0: \, p_1 - p_2 = 0 \quad H_a: \, p_1 - p_2 \geq 0 \) - \( \bigodot \, H_0: \, p_1 - p_2 = 0 \quad H_a: \, p_1 - p_2 < 0 \) (Selected) - \( \bigcirc \, H_0: \, p_1 - p_2 =
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