Question 1191680: How many subjects would be needed to ensure that a 95% confidence interval estimate of BMI had a margin of error not exceeding 3 units?
28 21 37 38 24 28 38 47 27 32 36 43
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate the required sample size:
**1. Identify the Key Values:**
* **Margin of Error (E):** 3 units
* **Confidence Level:** 95% This corresponds to a Z-score of 1.96.
* **Population Standard Deviation (σ):** Since we don't know the population standard deviation, we'll use the sample standard deviation as an estimate.
**2. Calculate the Sample Standard Deviation:**
First, calculate the mean of the given BMI values:
Mean = (28 + 21 + 37 + 38 + 24 + 28 + 38 + 47 + 27 + 32 + 36 + 43) / 12 = 32.58
Next, calculate the squared difference between each value and the mean, sum these squared differences, and divide by (n-1) to get the variance. Then take the square root to get the standard deviation.
Standard Deviation (s) ≈ 7.14 (You can use a calculator or spreadsheet software for this).
**3. Use the Sample Size Formula:**
The formula for calculating the sample size (n) is:
n = (Z * σ / E)²
Where:
* n = sample size
* Z = Z-score
* σ = population standard deviation (estimated by the sample standard deviation)
* E = margin of error
**4. Plug in the Values and Calculate:**
n = (1.96 * 7.14 / 3)²
n = (4.65)²
n ≈ 21.62
**5. Round Up:**
Since you can't have a fraction of a subject, always round the sample size up to the nearest whole number. Therefore, you would need 22 subjects.
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