Question 5 of 10 , Step 1 of 2 A random sample of 16 fields of spring wheat has a mean yield of 46.4 bushels per acre and standard deviation of 2.45 bushels per acre. Determine the \( 80 \% \) confidence interval for the true mean yield. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places. Answer

To find the critical value for an \(80\%\) confidence interval with a sample size of \(n=16\), we first need to determine the degrees of freedom, which is \(n-1 = 15\). For an \(80\%\) confidence level, we want to find the point in the t-distribution that leaves \(10\%\) in each tail (since \(100\% - 80\% = 20\%\), and half of that, \(10\%\), will be in each tail). Using a t-distribution table or calculator, we look up the critical value \(t_{\alpha/2}\) for \(15\) degrees of freedom and \(0.10\) in each tail. This critical value is approximately \(1.341\). Hence, the critical value we should use in constructing the confidence interval is \( \mathbf{1.341} \).