SOLUTION: A study was conducted to evaluate the hypothesis that tea consumption and premenstrual syndrome are associated. A total of 188 nursing students and 64 tea factory workers were give

Question 1200426: A study was conducted to evaluate the hypothesis that tea consumption and premenstrual syndrome are associated. A total of 188 nursing students and 64 tea factory workers were given questionnaires. The prevalence of premenstrual syndrome was 39% among the nursing students
and 77% among the tea factory workers. Calculate the 95% confidence interval for the prevalence of premenstrual syndrome for each of the two populations, nursing students and tea factory workers.

Answer by CPhill(1987) (Show Source): You can put this solution on YOUR website!
**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.

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