Question 1179666
Here's how to construct the 90% confidence interval for the population average difference in soft drink sales:

**1. Identify the Given Information:**

* Sample size (n): 21 stores
* Sample mean difference (x̄_diff): 75 cans
* Sample standard deviation of differences (s_diff): 30 cans
* Confidence level: 90%

**2. Determine the Degrees of Freedom:**

* Degrees of freedom (df) = n - 1 = 21 - 1 = 20

**3. Find the Critical t-Value:**

* Since we have a small sample size (n < 30) and we're using the sample standard deviation, we'll use a t-distribution.
* For a 90% confidence level and 20 degrees of freedom, the critical t-value (t*) is approximately 1.725. You can find this value using a t-table or a calculator.

**4. Calculate the Standard Error:**

* Standard error (SE) = s_diff / √n = 30 / √21 ≈ 6.547

**5. Calculate the Margin of Error:**

* Margin of error (ME) = t* * SE = 1.725 * 6.547 ≈ 11.30

**6. Construct the Confidence Interval:**

* Lower bound = x̄_diff - ME = 75 - 11.30 ≈ 63.70
* Upper bound = x̄_diff + ME = 75 + 11.30 ≈ 86.30

**7. State the Confidence Interval:**

* The 90% confidence interval is approximately (63.70, 86.30).

**Interpretation:**

We are 90% confident that the true population average difference in soft drink sales (increase) after the ad campaign is between 63.70 cans and 86.30 cans.