Find the critical $$ t $$-value for a $$ 90 \% $$ confidence interval using a $$ t $$-distribution with 16 degrees of freedom. Round your answer to three decimal places, if necessary.

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1. The confidence level is $$90\%$$, so the total probability in the two tails is
   $$
   \alpha = 1 - 0.90 = 0.10.
   $$

2. Since the distribution is symmetric, the probability in one tail is
   $$
   \frac{\alpha}{2} = \frac{0.10}{2} = 0.05.
   $$

3. Therefore, we need to find the $$ t $$-value such that the cumulative probability is
   $$
   1 - 0.05 = 0.95.
   $$
   This is denoted as $$ t_{0.95} $$.

4. Using a $$ t $$-distribution with $$16$$ degrees of freedom, we find that
   $$
   t_{0.95} \approx 1.746.
   $$

5. The critical $$ t $$-value for a $$ 90\% $$ confidence interval is approximately
   $$
   \boxed{1.746}.
   $$
The critical $$ t $$-value for a $$ 90\% $$ confidence interval with $$16$$ degrees of freedom is approximately $$1.746$$.

Find the critical \( t \)-value for a \( 90 \% \) confidence interval using a \( t \)-distribution with 16 degrees of freedom. Round your answer to three decimal places, if necessary.

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