(Solved): For parts a and b, use the t tables, software, or a calculator to estimate. For parts c and d, use ...

For parts $a$ and $b$, use the $t$ tables, software, or a calculator to estimate. For parts $c$ and $d$, use software or a calculator to estimate. a) the critical value of $t$ for a $95\%$ confidence interval with $df=12$. b) the critical value of $\mathrm{t}$ for a $90\%$ confidence interval with $\mathrm{df}=89$. c) the P-value for $t?2.73$ with 10 degrees of freedom. d) the P-value for $?t?>2.26$ with 28 degrees of freedom. Click the icon to view the $t$ table. a) What is the critical value of $t$ for a $95\%$ confidence interval with $df=12$ ? (Round to two decimal places as needed.) b) What is the critical value of $t$ for a $90\%$ confidence interval with $df=89$ ? (Round to two decimal places as needed.) c) What is the P-value for $t?2.73$ with 10 degrees of freedom? (Round to three decimal places as needed.) What is the P-value for $?t?>2.26$ with 28 degrees of freedom? \begin{tabular}{|c|c|c|c|c|c|c|} \hline \begin{tabular}{l} 32 \\ 35 \\ 40 \\ 45 \end{tabular} & \begin{tabular}{l} 1.309 \\ 1.306 \\ 1.303 \\ 1.301 \end{tabular} & \begin{tabular}{l} 1.694 \\ 1.690 \\ 1.684 \\ 1.679 \end{tabular} & \begin{tabular}{l} 2.037 \\ 2.030 \\ 2.021 \\ 2.014 \end{tabular} & \begin{tabular}{l} 2449 \\ 2438 \\ 2423 \\ 2412 \end{tabular} & \begin{tabular}{l} 2.738 \\ 2.725 \\ 2.704 \\ 2.690 \end{tabular} & \begin{tabular}{l} 32 \\ 35 \\ 40 \\ 45 \end{tabular} \\ \hline \begin{tabular}{r} 50 \\ 60 \\ 75 \\ 100 \\ 120 \end{tabular} & \begin{tabular}{l} 1.299 \\ 1.296 \\ 1.293 \\ 1.290 \\ 1.289 \end{tabular} & \begin{tabular}{l} 1.676 \\ 1.671 \\ 1.665 \\ 1.660 \\ 1.658 \end{tabular} & \begin{tabular}{l} 2.009 \\ 2.000 \\ 1.992 \\ 1.984 \\ 1.980 \end{tabular} & \begin{tabular}{r} 12.403 \\ 2.390 \\ 2.377 \\ 2.364 \\ 2.358 \end{tabular} & \begin{tabular}{l} 2.678 \\ 2.660 \\ 2.643 \\ 2.626 \\ 2.617 \end{tabular} & \begin{tabular}{r} 50 \\ 60 \\ 75 \\ 100 \\ 120 \end{tabular} \\ \hline \begin{tabular}{r} 140 \\ 180 \\ 250 \\ 400 \\ 1000 \end{tabular} & \begin{tabular}{l} 1.288 \\ 1.286 \\ 1.285 \\ 1.284 \\ 1.282 \end{tabular} & \begin{tabular}{l} 1.656 \\ 1.653 \\ 1.651 \\ 1.649 \\ 1.646 \end{tabular} & \begin{tabular}{l} 1.977 \\ 1.973 \\ 1.969 \\ 1.966 \\ 1.962 \end{tabular} & \begin{tabular}{l} 2.353 \\ 2.347 \\ 2.341 \\ 2.336 \\ 2.330 \end{tabular} & \begin{tabular}{l} 2.611 \\ 2.603 \\ 2.596 \\ 2.588 \\ 2.581 \end{tabular} & \begin{tabular}{r} 140 \\ 180 \\ 250 \\ 400 \\ 1000 \end{tabular} \\ \hline$?$ & 1.282 & 1.645 & 1.960 & 2.326 & 2576 & $?$ \\ \hline Confidencelevels & $80\%$ & $90\%$ & $95\%$ & $98\%$ & C. $99\%$ & \\ \hline \begin{tabular}{l} Two-tail probability \\ One-tail probability \end{tabular} & \begin{tabular}{l} 0.20 \\ 0.10 \end{tabular} & \begin{tabular}{l} 0.10 \\ 0.05 \end{tabular} & \begin{tabular}{c} 0.05 \\ 0.025 \end{tabular} & \begin{tabular}{l} 0.02 \\ 0.01 \end{tabular} & \begin{tabular}{l} 0.01 \\ 0.005 \end{tabular} & \\ \hline \end{tabular}