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13.2: A | Statistical Table- Student t Distribution

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    Student's \(t\) Distribution

    Figure A3 Upper critical values of Student's t Distribution with v Degrees of Freedom

    For selected probabilities, a, the table shows the values \(t_{v,a}\) such that \(P(t_v > t_{v,a}) = a\), where \(t_v\) is a Student’s \(t\) random variable with \(v\) degrees of freedom. For example, the probability is .10 that a Student’s \(t\) random variable with 10 degrees of freedom exceeds 1.372.

    \(v\) 0.10 0.05 0.025 0.01 0.005 0.001
    1 3.078 6.314 12.706 31.821 63.657 318.313
    2 1.886 2.920 4.303 6.965 9.925 22.327
    3 1.638 2.353 3.182 4.541 5.841 10.215
    4 1.533 2.132 2.776 3.747 4.604 7.173
    5 1.476 2.015 2.571 3.365 4.032 5.893
    6 1.440 1.943 2.447 3.143 3.707 5.208
    7 1.415 1.895 2.365 2.998 3.499 4.782
    8 1.397 1.860 2.306 2.896 3.355 4.499
    9 1.383 1.833 2.262 2.821 3.250 4.296
    10 1.372 1.812 2.228 2.764 3.169 4.143
    11 1.363 1.796 2.201 2.718 3.106 4.024
    12 1.356 1.782 2.179 2.681 3.055 3.929
    13 1.350 1.771 2.160 2.650 3.012 3.852
    14 1.345 1.761 2.145 2.624 2.977 3.787
    15 1.341 1.753 2.131 2.602 2.947 3.733
    16 1.337 1.746 2.120 2.583 2.921 3.686
    17 1.333 1.740 2.110 2.567 2.898 3.646
    18 1.330 1.734 2.101 2.552 2.878 3.610
    19 1.328 1.729 2.093 2.539 2.861 3.579
    20 1.325 1.725 2.086 2.528 2.845 3.552
    21 1.323 1.721 2.080 2.518 2.831 3.527
    22 1.321 1.717 2.074 2.508 2.819 3.505
    23 1.319 1.714 2.069 2.500 2.807 3.485
    24 1.318 1.711 2.064 2.492 2.797 3.467
    25 1.316 1.708 2.060 2.485 2.787 3.450
    26 1.315 1.706* 2.056 2.479 2.779 3.435
    27 1.314 1.703 2.052 2.473 2.771 3.421
    28 1.313 1.701 2.048 2.467 2.763 3.408
    29 1.311 1.699 2.045 2.462 2.756 3.396
    30 1.310 1.697 2.042 2.457 2.750 3.385
    40 1.303 1.684 2.021 2.423 2.704 3.307
    60 1.296 1.671 2.000 2.390 2.660 3.232
    100 1.290 1.660 1.984 2.364 2.626 3.174
    ∞ 1.282 1.645 1.960 2.326 2.576 3.090

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