Use 9 The \( t \) Distribution Table to find the \( t_{\alpha / 2} \) value for a \( 98 \% \) confidence interval for the mean when the sample size is 17.

To find the \( t_{\alpha/2} \) value for a \( 98\% \) confidence interval with a sample size of \( 17 \), we first calculate the degrees of freedom, which is \( n - 1 = 17 - 1 = 16 \). For a \( 98\% \) confidence level, the significance level \( \alpha = 1 - 0.98 = 0.02 \). Therefore, \( \alpha/2 = 0.01 \). Consulting the \( t \) distribution table for \( 16 \) degrees of freedom and \( \alpha/2 = 0.01 \), we find that the critical value \( t_{0.01, 16} \) is approximately \( 2.600 \). This means that for your confidence interval, you will be using a \( t \) value of about \( 2.600 \). Another fun fact: the \( t \) distribution is particularly helpful in statistics when working with smaller sample sizes (like yours!) because it accounts for the added variability in estimating the population standard deviation. So, next time you're in a group of 17, remember—you're part of a statistical powerhouse!