(a) Find the t-value such that the area in the right tail is 0.20 with 26 degrees of freedom. (Round to three decimal places as needed.) (b) Find the t-value such that the area in the right tail is 0.01 with 20 degrees of freedom. (Round to three decimal places as needed.) (c) Find the t-value such that the area left of the t-value is 0.025 with 8 degrees of freedom. [Hint: Use symmetry.] (Round to three decimal places as needed.) (d) Find the critical t-value that corresponds to 96% confidence. Assume 8 degrees of freedom. (Round to three decimal places as needed.)

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question

27

Determine the t-value in each of the cases.
Click the icon to view the table of areas under the t-distribution.
.....
(a) Find the t-value such that the area in the right tail is 0.20 with 26 degrees of freedom.
(Round to three decimal places as needed.)
(b) Find the t-value such that the area in the right tail is 0.01 with 20 degrees of freedom.
(Round to three decimal places as needed.)
(c) Find the t-value such that the area left of the t-value is 0.025 with 8 degrees of freedom. [Hint: Use symmetry.]
(Round to three decimal places as needed.)
(d) Find the critical t-value that corresponds to 96% confidence. Assume 8 degrees of freedom.
(Round to three decimal places as needed.)
Transcribed Image Text:Determine the t-value in each of the cases. Click the icon to view the table of areas under the t-distribution. ..... (a) Find the t-value such that the area in the right tail is 0.20 with 26 degrees of freedom. (Round to three decimal places as needed.) (b) Find the t-value such that the area in the right tail is 0.01 with 20 degrees of freedom. (Round to three decimal places as needed.) (c) Find the t-value such that the area left of the t-value is 0.025 with 8 degrees of freedom. [Hint: Use symmetry.] (Round to three decimal places as needed.) (d) Find the critical t-value that corresponds to 96% confidence. Assume 8 degrees of freedom. (Round to three decimal places as needed.)
Area in
right tail
Table VI
t-Distribution
Area in Right Tail
df
0.25
0.20
0.15
0.10
0.05
0.025
0.02
0.01
0.005
0.0025
0.001
0.0005
1.963
1.386
1.250
1.190
1.156
3.078
1.886
31.821
1.376
1.061
0.978
0.941
0.920
127.321
14.089
7.453
5.598
4.773
6.314
2.920
63.657
9.925
5.841
4.604
4.032
636.619
31.599
12.924
8.610
6.869
1
1.000
12.706
4.303
3.182
15.894
4.849
3.482
2.999
2.757
318.309
22.327
10.215
7.173
2
0.816
6.965
0.765
0.741
5
2.353
2.132
2.015
3
1.638
1.533
1.476
2.776
2.571
4.541
3.747
0.727
3.365
5.893
1.134
1.119
1.108
1.100
1.093
1.943
1.895
1.860
2.447
2.365
2.306
2.262
2.228
2.612
2.517
2.449
2.398
2.359
5.208
4.785
4.501
4.297
4.144
3.143
3.707
3.499
3.355
3.250
3.169
5.959
5.408
5.041
4.781
6
0.718
0.711
8
0.906
1.440
0.896
0.889
0.883
0.879
1.415
1.397
1.383
1.372
2.998
2.896
2.821
2.764
4.317
4.029
3.833
3.690
3.581
7
0.706
0.703
0.700
1.833
1.812
9
10
4.587
1.088
1.083
1.079
1.076
1.074
2.201
2.179
2.160
2.145
2.131
11
12
1.363
1.356
0.697
0.876
1.796
1.782
2.328
2.303
2.282
2.264
2.249
2.718
3.106
3.055
3.012
2.977
2.947
3.497
4.025
3.930
4.437
0.695
0.694
0.692
0.691
0.873
0.870
0.868
0.866
1.350
1.345
1.341
2.681
2.650
2.624
2.602
3.428
3.372
3.326
3.286
4.318
4.221
4.140
4.073
1.771
1.761
3.852
3.787
3.733
13
14
15
1.753
2.921
2.898
2.878
0.690
16
17
18
0.865
0.863
0.862
0.861
0.860
1.071
1.069
1.067
1.066
1.064
2.120
2.110
2.101
2.235
2.224
2.214
2.205
2.197
3.252
3.222
3.197
3.174
3.153
3.686
3.646
3.610
1.337
1.746
2.583
2.567
2.552
2.539
2.528
4.015
0.689
0.688
0.688
0.687
1.333
1.330
1.328
1.325
1.740
1.734
1.729
1.725
3.965
3.922
3.883
3.850
2.861
2.845
3.579
3.552
19
2.093
20
2.086
0.859
0.858
1.323
1.321
1.319
1.318
1.721
1.717
1.714
2.080
2.074
2.069
2.064
2.060
2.189
2.183
2.177
2.831
2.819
2.807
3.135
3.119
3.104
3.527
3.505
3.485
3.467
3.450
3.819
3.792
21
0.686
1.063
2.518
22
0.686
1.061
2.508
23
24
0.685
0.685
0.684
0.858
0.857
0.856
3.768
3.745
3.725
1.060
2.500
1.059
1.058 1.316 1.708
2.172
2.167
2.797
2.787
3.091
3.078
1.711
2.492
25
2.485
0.684
0.684
0.856
0.855
2.056
2.162
2.158
3.067
3.707
3.690
3.674
3.659
3.646
26
1.706
1.703
0.855 1.056 1.313 1.701
1.055 1.311 1.699
1.697
1.058 1.315
2.479
2.779
2.473
2.467
2.462
2.771
2.763
2.756
2.750
3.435
3.421
3.408
3.396
27
1.057 1.314
28
29
30
2.052
2.048
2.045
2.042
2.154
2.150
2.147
3.057
3.047
3.038
3.030
0.683
0.683
0.854
0.854
0.683
1.055
1.310
2.457
3.385
2.144
2.141
2.138
2.136
2.133
2.744
2.738
0.682
0.682
0.682
0.682
0.682
3.022
3.015
3.008
3.002
2.996
0.853
0.853
1.309
1.309
2.040
2.037
2.035
2.032
2.030
2.453
2.449
2.445
2.441
2.438
3.375
3.365
3.356
3.348
3.340
3.633
3.622
3.611
3.601
3.591
31
32
1.054
1.696
1.694
0.853
0.852
0.852
1.054
1.053
1.052
1.052
33
1.308
1.307
1.306
1.692
1.691
1.690
2.733
2.728
2.724
34
35
36
37
38
0.852
0.851
0.851
1.052
1.051
1.051
1.306
1.305
1.304
1.688
1.687
1.686
2.131
2.129
2.719
2.715
2.990
2.985
2.980
3.333
3.326
3.319
3.582
3.574
3.566
0.681
2.028
2.026
2.024
2.434
0.681
0.681
2.431
2.429
2.127
2.712
Transcribed Image Text:Area in right tail Table VI t-Distribution Area in Right Tail df 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 1.963 1.386 1.250 1.190 1.156 3.078 1.886 31.821 1.376 1.061 0.978 0.941 0.920 127.321 14.089 7.453 5.598 4.773 6.314 2.920 63.657 9.925 5.841 4.604 4.032 636.619 31.599 12.924 8.610 6.869 1 1.000 12.706 4.303 3.182 15.894 4.849 3.482 2.999 2.757 318.309 22.327 10.215 7.173 2 0.816 6.965 0.765 0.741 5 2.353 2.132 2.015 3 1.638 1.533 1.476 2.776 2.571 4.541 3.747 0.727 3.365 5.893 1.134 1.119 1.108 1.100 1.093 1.943 1.895 1.860 2.447 2.365 2.306 2.262 2.228 2.612 2.517 2.449 2.398 2.359 5.208 4.785 4.501 4.297 4.144 3.143 3.707 3.499 3.355 3.250 3.169 5.959 5.408 5.041 4.781 6 0.718 0.711 8 0.906 1.440 0.896 0.889 0.883 0.879 1.415 1.397 1.383 1.372 2.998 2.896 2.821 2.764 4.317 4.029 3.833 3.690 3.581 7 0.706 0.703 0.700 1.833 1.812 9 10 4.587 1.088 1.083 1.079 1.076 1.074 2.201 2.179 2.160 2.145 2.131 11 12 1.363 1.356 0.697 0.876 1.796 1.782 2.328 2.303 2.282 2.264 2.249 2.718 3.106 3.055 3.012 2.977 2.947 3.497 4.025 3.930 4.437 0.695 0.694 0.692 0.691 0.873 0.870 0.868 0.866 1.350 1.345 1.341 2.681 2.650 2.624 2.602 3.428 3.372 3.326 3.286 4.318 4.221 4.140 4.073 1.771 1.761 3.852 3.787 3.733 13 14 15 1.753 2.921 2.898 2.878 0.690 16 17 18 0.865 0.863 0.862 0.861 0.860 1.071 1.069 1.067 1.066 1.064 2.120 2.110 2.101 2.235 2.224 2.214 2.205 2.197 3.252 3.222 3.197 3.174 3.153 3.686 3.646 3.610 1.337 1.746 2.583 2.567 2.552 2.539 2.528 4.015 0.689 0.688 0.688 0.687 1.333 1.330 1.328 1.325 1.740 1.734 1.729 1.725 3.965 3.922 3.883 3.850 2.861 2.845 3.579 3.552 19 2.093 20 2.086 0.859 0.858 1.323 1.321 1.319 1.318 1.721 1.717 1.714 2.080 2.074 2.069 2.064 2.060 2.189 2.183 2.177 2.831 2.819 2.807 3.135 3.119 3.104 3.527 3.505 3.485 3.467 3.450 3.819 3.792 21 0.686 1.063 2.518 22 0.686 1.061 2.508 23 24 0.685 0.685 0.684 0.858 0.857 0.856 3.768 3.745 3.725 1.060 2.500 1.059 1.058 1.316 1.708 2.172 2.167 2.797 2.787 3.091 3.078 1.711 2.492 25 2.485 0.684 0.684 0.856 0.855 2.056 2.162 2.158 3.067 3.707 3.690 3.674 3.659 3.646 26 1.706 1.703 0.855 1.056 1.313 1.701 1.055 1.311 1.699 1.697 1.058 1.315 2.479 2.779 2.473 2.467 2.462 2.771 2.763 2.756 2.750 3.435 3.421 3.408 3.396 27 1.057 1.314 28 29 30 2.052 2.048 2.045 2.042 2.154 2.150 2.147 3.057 3.047 3.038 3.030 0.683 0.683 0.854 0.854 0.683 1.055 1.310 2.457 3.385 2.144 2.141 2.138 2.136 2.133 2.744 2.738 0.682 0.682 0.682 0.682 0.682 3.022 3.015 3.008 3.002 2.996 0.853 0.853 1.309 1.309 2.040 2.037 2.035 2.032 2.030 2.453 2.449 2.445 2.441 2.438 3.375 3.365 3.356 3.348 3.340 3.633 3.622 3.611 3.601 3.591 31 32 1.054 1.696 1.694 0.853 0.852 0.852 1.054 1.053 1.052 1.052 33 1.308 1.307 1.306 1.692 1.691 1.690 2.733 2.728 2.724 34 35 36 37 38 0.852 0.851 0.851 1.052 1.051 1.051 1.306 1.305 1.304 1.688 1.687 1.686 2.131 2.129 2.719 2.715 2.990 2.985 2.980 3.333 3.326 3.319 3.582 3.574 3.566 0.681 2.028 2.026 2.024 2.434 0.681 0.681 2.431 2.429 2.127 2.712
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