To find the critical value $t_{\alpha/2}$ for a 95.5% confidence level, we can break down the problem as follows:

1. Confidence Level (CL): 95.5%, which implies a significance level $\alpha = 1 - 0.955 = 0.045$.
2. Degrees of Freedom (df): Since the sample size is 20, we have $df = n - 1 = 19$.
3. Two-Tailed Test: For a two-tailed confidence interval, we are interested in $\alpha/2 = 0.045 / 2 = 0.0225$ for each tail.

Now, we need the $t$-value that leaves 2.25% in each tail with 19 degrees of freedom. Using a $t$-table or statistical software:

$t_{\alpha/2} \approx \pm 2.197$

Answer: The critical value $t_{\alpha/2} = \pm 2.197$.

Would you like a deeper explanation or have further questions?

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Additional Related Questions

1. How does the choice of sample size affect the confidence interval's width?
2. What is the interpretation of a 95.5% confidence level?
3. How would the critical value change if the confidence level were set to 99%?
4. What if we assumed a population that was not normally distributed?
5. How does the sample size influence the accuracy of the t-distribution approximation?

Tip: Remember, as sample sizes increase, the t-distribution approaches the standard normal distribution (z-distribution).