Question 1186540
Here's how to calculate a 95% confidence interval for the mean economic dynamism of middle-income countries based on the provided data:

**1. Calculate the Sample Mean (x̄):**

Sum all the economic dynamism values and divide by the number of values (n = 25).

x̄ = (25.8057 + 37.4511 + ... + 21.6643) / 25
x̄ ≈ 43.8727

**2. Calculate the Sample Standard Deviation (s):**

This measures the spread of the data.  You can use a calculator or statistical software to find this.

s ≈ 9.5626

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

Since the sample size is small (n < 30), we use the t-distribution.  For a 95% confidence level and 24 degrees of freedom (n - 1 = 25 - 1 = 24), the critical t-value is approximately 2.064. You can find this using a t-table or a statistical calculator.

**4. Calculate the Margin of Error (ME):**

ME = t * (s / √n)
ME = 2.064 * (9.5626 / √25)
ME ≈ 3.9934

**5. Calculate the Confidence Interval:**

*   Lower Bound = x̄ - ME = 43.8727 - 3.9934 ≈ 39.8793
*   Upper Bound = x̄ + ME = 43.8727 + 3.9934 ≈ 47.8661

**Result:**

The 95% confidence interval for the mean economic dynamism of middle-income countries is approximately (39.8793, 47.8661).

**Interpretation:**

We are 95% confident that the true mean economic dynamism for all middle-income countries lies within this interval. This means that if we were to repeat this study many times, 95% of the calculated confidence intervals would contain the true population mean.