Question 1198350
**1. Calculate Sample Proportions**

* **Proportion of Male Customers Preferring Coke:**
    * p1 = (Number of Male Customers Preferring Coke) / (Total Number of Male Customers)
    * p1 = 72 / 130 
    * p1 = 0.5538

* **Proportion of Female Customers Preferring Coke:**
    * p2 = (Number of Female Customers Preferring Coke) / (Total Number of Female Customers)
    * p2 = 38 / 70 
    * p2 = 0.5429

**2. Calculate the Difference in Sample Proportions**

* p̂1 - p̂2 = 0.5538 - 0.5429 
* p̂1 - p̂2 = 0.0109

**3. Calculate Pooled Proportion**

* Pooled Proportion (p̂) = [(Number of Male Customers Preferring Coke) + (Number of Female Customers Preferring Coke)] / (Total Number of Male Customers + Total Number of Female Customers)
* p̂ = (72 + 38) / (130 + 70)
* p̂ = 110 / 200
* p̂ = 0.55

**4. Calculate Standard Error**

* Standard Error (SE) = √[p̂ * (1 - p̂) * ((1/n1) + (1/n2))]
    * where n1 = number of male customers, n2 = number of female customers
* SE = √[0.55 * (1 - 0.55) * ((1/130) + (1/70))]
* SE ≈ 0.0628

**5. Determine Critical Value**

* For a 95% confidence interval, the critical value (z*) from the standard normal distribution is 1.96.

**6. Calculate Margin of Error**

* Margin of Error = z* * SE
* Margin of Error = 1.96 * 0.0628
* Margin of Error ≈ 0.1231

**7. Construct the 95% Confidence Interval**

* Lower Limit: (p̂1 - p̂2) - Margin of Error = 0.0109 - 0.1231 = -0.1122
* Upper Limit: (p̂1 - p̂2) + Margin of Error = 0.0109 + 0.1231 = 0.1340

**Therefore, the 95% confidence interval for the difference between the proportions of male and female customers who prefer Coke Classic over Pepsi Cola is (-0.1122, 0.1340).**

**Interpretation:**

* Since the confidence interval includes zero, we cannot conclude with 95% confidence that there is a statistically significant difference between the proportions of male and female customers who prefer Coke Classic over Pepsi Cola in Chicago. 
* It's possible that the observed difference in proportions is due to random chance.