For \( C=95 \% \) if \( \sigma=7.21 \) and \( \mathrm{E}=2 \) then Sample Size \( n=35 \)

To determine the necessary sample size for a 95% confidence level with a desired margin of error (E) of 2 and known population standard deviation (\( \sigma \)) of 7.21, we can use the formula for sample size in estimating the mean: \[ n = \left( \frac{Z \cdot \sigma}{E} \right)^2 \] For a 95% confidence level, the Z-value is approximately 1.96. Plugging in the values: \[ n = \left( \frac{1.96 \cdot 7.21}{2} \right)^2 \approx \left( \frac{14.1516}{2} \right)^2 \approx (7.0758)^2 \approx 50.14 \] Thus, the required sample size is approximately 51. If you used 35, it's on the lower side for the desired parameters, which could affect the precision of your estimates. To make the most of your sample size, remember that sample size isn't just about the numbers; it's about the power of your results! A larger sample size can reduce variability and increase the reliability of your estimates. Always assess the trade-off between resource availability and the confidence you want in your results.