To find the critical value ($z^*$) necessary for a confidence interval at a confidence level of $c = 0.96$:

1. The level of significance, $\alpha$, is $1 - c = 1 - 0.96 = 0.04$.
2. Since a confidence interval is two-tailed, divide $\alpha$ by 2: $\alpha/2 = 0.02$.
3. Find the z-value corresponding to the cumulative area of $1 - 0.02 = 0.98$ in the standard normal distribution.

From the z-table or a calculator, the critical z-value is approximately:

$z^* \approx 2.05$

Would you like to see how this applies to specific confidence interval calculations?

Related Questions:

1. How does the critical value change with a different confidence level, such as $c = 0.90$ or $c = 0.99$?
2. How is the critical value used in constructing confidence intervals for means or proportions?
3. What is the critical value for a t-distribution with a confidence level of $c = 0.96$ and a sample size of 15?
4. How does the critical value relate to the margin of error?
5. Can you explain the difference between z-scores and t-scores in confidence intervals?

Tip: Always ensure the appropriate distribution (z or t) is used based on the sample size and standard deviation availability.