Question 1192382
**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.