Question 1200426
**1. Nursing Students**

* **Sample Size (n1):** 188
* **Prevalence of PMS (p1):** 39% = 0.39
* **Number of Students with PMS (x1):** 188 * 0.39 = 73.32 ≈ 73 

* **Standard Error (SE1):** 
    * SE1 = √[p1 * (1 - p1) / n1] 
    * SE1 = √[0.39 * (1 - 0.39) / 188] 
    * SE1 ≈ 0.0394

* **95% Confidence Interval:** 
    * For a 95% confidence level, the z-score is 1.96.
    * Lower Limit: p1 - (z * SE1) = 0.39 - (1.96 * 0.0394) ≈ 0.313 
    * Upper Limit: p1 + (z * SE1) = 0.39 + (1.96 * 0.0394) ≈ 0.467

* **95% Confidence Interval for Nursing Students:** (0.313, 0.467)

**2. Tea Factory Workers**

* **Sample Size (n2):** 64
* **Prevalence of PMS (p2):** 77% = 0.77
* **Number of Students with PMS (x2):** 64 * 0.77 = 49.28 ≈ 49 

* **Standard Error (SE2):** 
    * SE2 = √[p2 * (1 - p2) / n2] 
    * SE2 = √[0.77 * (1 - 0.77) / 64] 
    * SE2 ≈ 0.0534

* **95% Confidence Interval:** 
    * Lower Limit: p2 - (z * SE2) = 0.77 - (1.96 * 0.0534) ≈ 0.665 
    * Upper Limit: p2 + (z * SE2) = 0.77 + (1.96 * 0.0534) ≈ 0.875

* **95% Confidence Interval for Tea Factory Workers:** (0.665, 0.875)

**Interpretation:**

* We are 95% confident that the true proportion of nursing students experiencing PMS lies between 31.3% and 46.7%.
* We are 95% confident that the true proportion of tea factory workers experiencing PMS lies between 66.5% and 87.5%.

These confidence intervals provide a range within which the true population proportions are likely to fall. 

**Note:**

* These calculations assume that the samples are representative of the respective populations.
* Larger sample sizes would generally lead to narrower confidence intervals and more precise estimates.