For \( C=95 \% \) If \( \sigma=7.21 \) and \( \mathrm{n}=35 \) then \( E=4.12 \)

When you have a confidence level of \( C = 95 \% \), it indicates that you're quite certain about your interval containing the true population parameter. This is achieved using the Z-score corresponding to 95% confidence, which is approximately \( 1.96 \). With \( \sigma = 7.21 \) and \( n = 35 \), you can determine the margin of error by calculating \( E = Z \times \frac{\sigma}{\sqrt{n}} \). Plugging in the values, you can calculate whether the provided \( E = 4.12 \) aligns with this setup. To enhance your grasp of margins of error, consider experimenting with different sample sizes or confidence levels. For instance, as your sample size increases, the margin of error typically decreases, leading to a more precise estimate of the population parameter. Adjusting the confidence level will also affect how wide or narrow your confidence interval appears. Give it a try, and see how the numbers dance!