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Question 1186540: The economic dynamism, which is the index of productive growth in dollars for countries that are designated by the World Bank as middle-income are in table #8.3.9 ("SOCR data 2008," 2013). Compute a 95% confidence interval for the mean economic dynamism of middle-income countries.
Table #8.3.9: Economic Dynamism ($) of Middle Income Countries
25.8057 37.4511 51.915 43.6952 47.8506 43.7178 58.0767
41.1648 38.0793 37.7251 39.6553 42.0265 48.6159 43.8555
49.1361 61.9281 41.9543 44.9346 46.0521 48.3652 43.6252
50.9866 59.1724 39.6282 33.6074 21.6643
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! 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.
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