To find $t_c$ for a 0.95 confidence level when the sample size is 19:

1. Determine the degrees of freedom (df): Degrees of freedom ($df$) is calculated as $n - 1$, where $n$ is the sample size.
   $df = 19 - 1 = 18$.

2. Locate the appropriate column for 0.95 confidence level: For a confidence level of 0.95 in a two-tailed test, look under the column where $c = 0.950$ (this corresponds to $\text{two-tail area} = 0.05$).

3. Read the table value: For $df = 18$ and $c = 0.950$, the critical $t$-value is 2.101.

Final Answer:

The $t_c$ value is 2.101 (rounded to three decimal places).

Do you want further clarification on this process, or assistance with similar problems?

Here are 5 questions to deepen your understanding:

1. What happens to the $t_c$ value as the sample size increases?
2. How would the calculation differ for a one-tailed test?
3. Why is the confidence level related to the tail area?
4. What are the implications of using $t$-values instead of $z$-values?
5. How does the degree of freedom impact the critical value?

Tip: Always match the tail area and degrees of freedom carefully to avoid errors in looking up the critical value.