Question 1192440
**1. Calculate the Sample Proportions**

* **Drug 1:** 
    * Sample proportion (p1) = 750 / 1000 = 0.75 

* **Drug 2:** 
    * Sample proportion (p2) = 800 / 1000 = 0.80

**2. Calculate the Standard Error**

* **Pooled Proportion (p̂):** 
    * p̂ = (Number of successes in both samples) / (Total sample size) 
    * p̂ = (750 + 800) / (1000 + 1000) = 1550 / 2000 = 0.775

* **Standard Error (SE):**
    * SE = √[p̂ * (1 - p̂) * (1/n1 + 1/n2)] 
    * SE = √[0.775 * (1 - 0.775) * (1/1000 + 1/1000)] 
    * SE = √[0.775 * 0.225 * (2/1000)] 
    * SE ≈ 0.0186

**3. Determine the Z-score for 90% Confidence Level**

* For a 90% confidence interval, the Z-score is 1.645.

**4. Calculate the Margin of Error**

* Margin of Error (ME) = Z-score * SE 
* ME = 1.645 * 0.0186 
* ME ≈ 0.0306

**5. Construct the Confidence Intervals**

* **Drug 1:**
    * Lower limit: p1 - ME = 0.75 - 0.0306 = 0.7194
    * Upper limit: p1 + ME = 0.75 + 0.0306 = 0.7806
    * 90% CI for Drug 1: (0.7194, 0.7806)

* **Drug 2:**
    * Lower limit: p2 - ME = 0.80 - 0.0306 = 0.7694
    * Upper limit: p2 + ME = 0.80 + 0.0306 = 0.8306
    * 90% CI for Drug 2: (0.7694, 0.8306)

**Interpretation:**

* We are 90% confident that the true proportion of individuals who experience pain relief with Drug 1 lies between 71.94% and 78.06%.
* We are 90% confident that the true proportion of individuals who experience pain relief with Drug 2 lies between 76.94% and 83.06%.

**Note:**

* These confidence intervals provide a range of plausible values for the true population proportions. 
* The intervals do not overlap, suggesting that there might be a statistically significant difference in the effectiveness of the two drugs. However, further statistical analysis (such as a hypothesis test) would be needed to confirm this.

**Disclaimer:** 

* This analysis provides a basic framework for constructing confidence intervals. 
* In real-world scenarios, more sophisticated statistical methods might be necessary, especially when dealing with medical data. 
* This information should not be considered medical advice.