Math  /  Data & Statistics

Question2. Find the required sample size for 95%95 \% confidence level with a margin of error of 4%4 \% and standard deviation =0.35=0.35.

Studdy Solution
Use the formula for the sample size n n :
n=(zσE)2 n = \left( \frac{z \cdot \sigma}{E} \right)^2
where: - z=1.96 z = 1.96 (critical value from STEP_1), - σ=0.35 \sigma = 0.35 (standard deviation), - E=0.04 E = 0.04 (margin of error).
Substitute the values into the formula:
n=(1.960.350.04)2 n = \left( \frac{1.96 \cdot 0.35}{0.04} \right)^2
Calculate the expression inside the parentheses:
n=(0.6860.04)2 n = \left( \frac{0.686}{0.04} \right)^2
n=(17.15)2 n = (17.15)^2
Calculate the square:
n294.72 n \approx 294.72
Since the sample size must be a whole number, round up to the nearest whole number:
n=295 n = 295
The required sample size is:
295 \boxed{295}

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