Economics - Hypothesis

ISBN: 0073401803 Author: Lind, Marchal, Wathen Title: Statistical Techniques in Business & Economics

Fifteenth edition

Back endsheets Color: 4 Pages: 5

Student’s t Distribution

0 0

1 2� �� �

1 2

Confidence interval t–t 0

Left-tailed test –t t

Right-tailed test t

Two-tailed test t–t

Confidence Intervals, c

80% 90% 95% 98% 99% 99.9%

Level of Significance for One-Tailed Test, �

0.10 0.05 0.025 0.01 0.005 0.0005

Level of Significance for Two-Tailed Test, �

0.20 0.10 0.05 0.02 0.01 0.001

1 3.078 6.314 12.706 31.821 63.657 636.619 2 1.886 2.920 4.303 6.965 9.925 31.599 3 1.638 2.353 3.182 4.541 5.841 12.924 4 1.533 2.132 2.776 3.747 4.604 8.610 5 1.476 2.015 2.571 3.365 4.032 6.869

6 1.440 1.943 2.447 3.143 3.707 5.959 7 1.415 1.895 2.365 2.998 3.499 5.408 8 1.397 1.860 2.306 2.896 3.355 5.041 9 1.383 1.833 2.262 2.821 3.250 4.781

10 1.372 1.812 2.228 2.764 3.169 4.587

11 1.363 1.796 2.201 2.718 3.106 4.437 12 1.356 1.782 2.179 2.681 3.055 4.318 13 1.350 1.771 2.160 2.650 3.012 4.221 14 1.345 1.761 2.145 2.624 2.977 4.140 15 1.341 1.753 2.131 2.602 2.947 4.073

16 1.337 1.746 2.120 2.583 2.921 4.015 17 1.333 1.740 2.110 2.567 2.898 3.965 18 1.330 1.734 2.101 2.552 2.878 3.922 19 1.328 1.729 2.093 2.539 2.861 3.883 20 1.325 1.725 2.086 2.528 2.845 3.850

21 1.323 1.721 2.080 2.518 2.831 3.819 22 1.321 1.717 2.074 2.508 2.819 3.792 23 1.319 1.714 2.069 2.500 2.807 3.768 24 1.318 1.711 2.064 2.492 2.797 3.745 25 1.316 1.708 2.060 2.485 2.787 3.725

26 1.315 1.706 2.056 2.479 2.779 3.707 27 1.314 1.703 2.052 2.473 2.771 3.690 28 1.313 1.701 2.048 2.467 2.763 3.674 29 1.311 1.699 2.045 2.462 2.756 3.659 30 1.310 1.697 2.042 2.457 2.750 3.646

31 1.309 1.696 2.040 2.453 2.744 3.633 32 1.309 1.694 2.037 2.449 2.738 3.622 33 1.308 1.692 2.035 2.445 2.733 3.611 34 1.307 1.691 2.032 2.441 2.728 3.601 35 1.306 1.690 2.030 2.438 2.724 3.591

Confidence Intervals, c

80% 90% 95% 98% 99% 99.9%

Level of Significance for One-Tailed Test, �

0.10 0.05 0.025 0.01 0.005 0.0005

Level of Significance for Two-Tailed Test, �

0.20 0.10 0.05 0.02 0.01 0.001

36 1.306 1.688 2.028 2.434 2.719 3.582 37 1.305 1.687 2.026 2.431 2.715 3.574 38 1.304 1.686 2.024 2.429 2.712 3.566 39 1.304 1.685 2.023 2.426 2.708 3.558 40 1.303 1.684 2.021 2.423 2.704 3.551

41 1.303 1.683 2.020 2.421 2.701 3.544 42 1.302 1.682 2.018 2.418 2.698 3.538 43 1.302 1.681 2.017 2.416 2.695 3.532 44 1.301 1.680 2.015 2.414 2.692 3.526 45 1.301 1.679 2.014 2.412 2.690 3.520

46 1.300 1.679 2.013 2.410 2.687 3.515 47 1.300 1.678 2.012 2.408 2.685 3.510 48 1.299 1.677 2.011 2.407 2.682 3.505 49 1.299 1.677 2.010 2.405 2.680 3.500 50 1.299 1.676 2.009 2.403 2.678 3.496

51 1.298 1.675 2.008 2.402 2.676 3.492 52 1.298 1.675 2.007 2.400 2.674 3.488 53 1.298 1.674 2.006 2.399 2.672 3.484 54 1.297 1.674 2.005 2.397 2.670 3.480 55 1.297 1.673 2.004 2.396 2.668 3.476

56 1.297 1.673 2.003 2.395 2.667 3.473 57 1.297 1.672 2.002 2.394 2.665 3.470 58 1.296 1.672 2.002 2.392 2.663 3.466 59 1.296 1.671 2.001 2.391 2.662 3.463 60 1.296 1.671 2.000 2.390 2.660 3.460

61 1.296 1.670 2.000 2.389 2.659 3.457 62 1.295 1.670 1.999 2.388 2.657 3.454 63 1.295 1.669 1.998 2.387 2.656 3.452 64 1.295 1.669 1.998 2.386 2.655 3.449 65 1.295 1.669 1.997 2.385 2.654 3.447

66 1.295 1.668 1.997 2.384 2.652 3.444 67 1.294 1.668 1.996 2.383 2.651 3.442 68 1.294 1.668 1.995 2.382 2.650 3.439 69 1.294 1.667 1.995 2.382 2.649 3.437 70 1.294 1.667 1.994 2.381 2.648 3.435

(continued )

df

(degrees of

freedom)

df

(degrees of

freedom)

(continued-top right ) (continued )

Lin01803_endsheet.indd Page 1 11/10/10 6:10 PM F-497Lin01803_endsheet.indd Page 1 11/10/10 6:10 PM F-497 208/MHBR192/ Lin 01803_ disk1of1/ 007340 1803/L in0 1803_p agefile s208/MHBR192/Lin01803_disk1of1/0073401803/Lin01803_pagefiles

ISBN: 0073401803 Author: Lind, Marchal, Wathen Title: Statistical Techniques in Business & Economics

Fifteenth edition

Back endsheets Color: 4 Pages: 6, 7

Confidence Intervals, c

80% 90% 95% 98% 99% 99.9%

Level of Significance for One-Tailed Test, �

0.10 0.05 0.025 0.01 0.005 0.0005

Level of Significance for Two-Tailed Test, �

0.20 0.10 0.05 0.02 0.01 0.001

71 1.294 1.667 1.994 2.380 2.647 3.433 72 1.293 1.666 1.993 2.379 2.646 3.431 73 1.293 1.666 1.993 2.379 2.645 3.429 74 1.293 1.666 1.993 2.378 2.644 3.427 75 1.293 1.665 1.992 2.377 2.643 3.425

76 1.293 1.665 1.992 2.376 2.642 3.423 77 1.293 1.665 1.991 2.376 2.641 3.421 78 1.292 1.665 1.991 2.375 2.640 3.420 79 1.292 1.664 1.990 2.374 2.640 3.418 80 1.292 1.664 1.990 2.374 2.639 3.416

81 1.292 1.664 1.990 2.373 2.638 3.415 82 1.292 1.664 1.989 2.373 2.637 3.413 83 1.292 1.663 1.989 2.372 2.636 3.412 84 1.292 1.663 1.989 2.372 2.636 3.410 85 1.292 1.663 1.988 2.371 2.635 3.409

86 1.291 1.663 1.988 2.370 2.634 3.407 87 1.291 1.663 1.988 2.370 2.634 3.406 88 1.291 1.662 1.987 2.369 2.633 3.405 89 1.291 1.662 1.987 2.369 2.632 3.403 90 1.291 1.662 1.987 2.368 2.632 3.402

91 1.291 1.662 1.986 2.368 2.631 3.401 92 1.291 1.662 1.986 2.368 2.630 3.399 93 1.291 1.661 1.986 2.367 2.630 3.398 94 1.291 1.661 1.986 2.367 2.629 3.397 95 1.291 1.661 1.985 2.366 2.629 3.396

96 1.290 1.661 1.985 2.366 2.628 3.395 97 1.290 1.661 1.985 2.365 2.627 3.394 98 1.290 1.661 1.984 2.365 2.627 3.393 99 1.290 1.660 1.984 2.365 2.626 3.392

100 1.290 1.660 1.984 2.364 2.626 3.390

120 1.289 1.658 1.980 2.358 2.617 3.373 140 1.288 1.656 1.977 2.353 2.611 3.361 160 1.287 1.654 1.975 2.350 2.607 3.352 180 1.286 1.653 1.973 2.347 2.603 3.345 200 1.286 1.653 1.972 2.345 2.601 3.340

� 1.282 1.645 1.960 2.326 2.576 3.291

Student’s t Distribution (concluded )

df

(degrees of

freedom)

(continued )

Areas under the Normal Curve

z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753 0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141 0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517 0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879

0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224 0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549 0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852 0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133 0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389

1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830 1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015 1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177 1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319

1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545 1.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633 1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706 1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767

2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817 2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857 2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890 2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916 2.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936

2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952 2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.4964 2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974 2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981 2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986

3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990

Example: If z = 1.96, then P (0 to z ) = 0.4750.

z 0 1.96

0.4750

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