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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To find the critical \( t \)-value for a \( 90\% \) confidence interval with \( 16 \) degrees of freedom, you can use a \( t \)-distribution table or a statistical calculator. For a \( 90\% \) confidence interval, you are looking for the \( t \)-value that corresponds to \( \alpha/2 = 0.05 \) because \( 1 - 0.90 = 0.10 \), and half of that is \( 0.05 \). After checking a \( t \)-distribution table or using a calculator, the critical \( t \)-value for \( 16 \) degrees of freedom at the \( 0.05 \) level is approximately \( 1.746 \). So, the critical \( t \)-value rounded to three decimal places is \( 1.746 \).
