Use at-table, software, or a calculator to estimate the following critical values.

a) The critical value of t for a 90% confidence interval with df=12.

b) The critical value of t for a 98% confidence interval with df=68.

Two-tail probability 0.20 0.10 0.05 0.02 0.01

One-tail probability 0.10 0.05 0.025 0.01 0.005

df - - - - -

1 3.078 6.314 12.706 31.821 63.657

2 1.886 2.920 4.303 6.965 9.925

3 1.638 2.353 3.182 4.541 5.841

4 1.533 2.132 2.776 3.747 4.604

5 1.476 2.015 2.571 3.365 4.032

6 1.440 1.943 2.447 3.143 3.707

7 1.415 1.895 2.365 2.998 3.499

8 1.397 1.860 2.306 2.896 3.355

9 1.383 1.833 2.262 2.821 3.250

10 1.372 1.812 2.228 2.764 3.169

11 1.363 1.796 2.201 2.718 3.106

12 1.356 1.782 2.179 2.681 3.055

13 1.350 1.771 2.160 2.650 3.012

14 1.345 1.761 2.145 2.624 2.977

15 1.341 1.753 2.131 2.602 2.947

16 1.337 1.746 2.120 2.583 2.921

17 1.333 1.740 2.110 2.567 2.898

18 1.330 1.734 2.101 2.552 2.878

19 1.328 1.729 2.093 2.539 2.861

20 1.325 1.725 2.086 2.528 2.845

21 1.323 1.721 2.080 2.518 2.831

22 1.321 1.717 2.074 2.508 2.819

23 1.319 1.714 2.069 2.500 2.807

24 1.318 1.711 2.064 2.492 2.797

25 1.316 1.708 2.060 2.485 2.787

26 1.315 1.706 2.056 2.479 2.779

27 1.314 1.703 2.052 2.473 2.771

28 1.313 1.701 2.048 2.467 2.763

29 1.311 1.699 2.045 2.462 2.756

30 1.310 1.697 2.042 2.457 2.750

32 1.309 1.694 2.037 2.449 2.738

35 1.306 1.690 2.030 2.438 2.725

40 1.303 1.684 2.021 2.423 2.704

45 1.301 1.679 2.014 2.412 2.690

50 1.299 1.676 2.009 2.403 2.678

60 1.296 1.671 2.000 2.390 2.660

75 1.293 1.665 1.992 2.377 2.643

100 1.290 1.660 1.984 2.364 2.626

120 1.289 1.658 1.980 2.358 2.617

140 1.288 1.656 1.977 2.353 2.611

180 1.286 1.653 1.973 2.347 2.603

250 1.285 1.651 1.969 2.341 2.596

400 1.284 1.649 1.966 2.336 2.588

1000 1.282 1.646 1.962 2.330 63.657

infinity 1.282 1.645 1.960 2.326 2.576

Confidence levels 80 90 95 98 99

a) What is the critical value of t for a 90% confidence interval with df=12?

(Round to two decimal places asneeded.)

b) What is the critical value of t for a 98% confidence interval with df=68?

(Round to two decimal places asneeded.)