Question 1192382: In an experiment designed to test the effectiveness of paroxetine for treating bipolar
depression, subjects were measured using the Hamilton Depression Scale with the results given below (based on data from ”Double-Blind, Placebo-Controlled Comparison
of Imipramine and Paroxetine in the Treatment of Bipolar Depression” by Nemeroff,
Evans, et al., American Journal of Psychiatry, Vol. 158, No. 6). use a 0.05 significance
level to test the claim that the treatment group and placebo group come from populations with the same mean. What does the result of the hypothesis test suggest about
paroxetine as a treatment for bipolar depression? (7 pts)
Placebo Group n = 43 x¯ = 21.57 s = 3.87
Paroxetine Treatment Group n = 33 x¯ = 20.38 s = 3.91
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **1. Set up Hypotheses**
* **Null Hypothesis (H0):** The mean Hamilton Depression Scale score for the placebo group is equal to the mean score for the paroxetine treatment group (μ1 = μ2).
* **Alternative Hypothesis (H1):** The mean Hamilton Depression Scale score for the placebo group is not equal to the mean score for the paroxetine treatment group (μ1 ≠ μ2).
**2. Perform Independent Samples t-test**
* We will use an independent samples t-test to compare the means of the two groups.
* Since the sample standard deviations are similar (3.87 and 3.91), we can assume equal variances for the t-test.
* **Calculate the t-statistic:**
* t = (x̄1 - x̄2) / √[(s1²/n1) + (s2²/n2)]
* where:
* x̄1 = mean of placebo group
* x̄2 = mean of treatment group
* s1 = standard deviation of placebo group
* s2 = standard deviation of treatment group
* n1 = sample size of placebo group
* n2 = sample size of treatment group
* t = (21.57 - 20.38) / √[(3.87²/43) + (3.91²/33)]
* t ≈ 1.323
* **Determine the degrees of freedom:**
* Degrees of freedom (df) = n1 + n2 - 2 = 43 + 33 - 2 = 74
* **Find the p-value:**
* Using a t-distribution table or statistical software, find the p-value associated with the calculated t-statistic (1.323) and 74 degrees of freedom.
* **Result:**
* The p-value is approximately 0.1900.
**3. Make a Decision**
* **Significance Level (α):** 0.05
* **Compare p-value to α:**
* Since the p-value (0.1900) is greater than the significance level (0.05), we **fail to reject the null hypothesis**.
**4. Conclusion**
* **Based on the results of the t-test, there is not enough evidence to suggest that paroxetine treatment is significantly different from placebo in reducing bipolar depression symptoms.**
* The observed difference in mean scores between the groups could be due to chance.
**Note:**
* This analysis assumes that the data meets the assumptions of the t-test, such as independent samples and normally distributed data.
* Further research and larger sample sizes may be needed to draw more definitive conclusions about the effectiveness of paroxetine for treating bipolar depression.
This analysis provides a framework for interpreting the results of the study.
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