Final answer:
To calculate the sample size required for a 95% confidence level with a margin of error and standard deviation given, use the formula n = (Z * σ / EBM)², where Z is the z-value corresponding to the confidence level, σ is the standard deviation, and EBM is the margin of error.
Step-by-step explanation:
To calculate the sample size required for a 95% confidence level, we need to use the formula: n = (Z * σ / EBM)², where Z is the z-value corresponding to the desired confidence level, σ is the standard deviation, and EBM is the desired margin of error.
In this case, Z = 1.96 (for a 95% confidence level), σ = 6, and EBM = 2. Plugging these values into the formula, we get: n = (1.96 * 6 / 2)² = 217.6
Since the sample size must be an integer, we round up to the next higher integer to ensure the sample size is large enough. Therefore, the required sample size is n = 218.