Question 1192314: with sample size of 900 the standard error is 3 what should be sample size so that we would be 95$ confident that population mean is within 4 sample of mean?
Answer by CPhill(2189)   (Show Source):
You can put this solution on YOUR website! **1. Determine the Z-score for 95% Confidence:**
* For a 95% confidence level, the Z-score is 1.96.
**2. Calculate the Standard Deviation:**
* Standard Error (SE) = Standard Deviation (σ) / √(sample size)
* 3 = σ / √900
* σ = 3 * √900
* σ = 3 * 30
* σ = 90
**3. Determine the Required Sample Size:**
* Margin of Error (E) = 4
* Z-score = 1.96
* Standard Deviation (σ) = 90
* Formula: n = (Z-score * σ / E)²
* n = (1.96 * 90 / 4)²
* n = (44.1)²
* n = 1944.81
* **Round up to the nearest whole number:** n = 1945
**Therefore, the required sample size to be 95% confident that the population mean is within 4 units of the sample mean is 1945.**
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