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 15 degrees of freedom. (Round to three decimal places as needed.) (b) Find the t-value such that the area in the right tail is 0.25 with 22 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 0.005 with 26 degrees of freedom. [Hint: Use symmetry.] (Round to three decimal places as needed.) (d) Find the critical t-value that corresponds to 90% confidence. Assume 14 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

9

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 15 degrees of freedom.
(Round to three decimal places as needed.)
(b) Find the t-value such that the area in the right tail is 0.25 with 22 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 0.005 with 26 degrees of freedom. [Hint: Use symmetry.]
(Round to three decimal places as needed.)
(d) Find the critical t-value that corresponds to 90% confidence. Assume 14 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 15 degrees of freedom. (Round to three decimal places as needed.) (b) Find the t-value such that the area in the right tail is 0.25 with 22 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 0.005 with 26 degrees of freedom. [Hint: Use symmetry.] (Round to three decimal places as needed.) (d) Find the critical t-value that corresponds to 90% confidence. Assume 14 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
63.657
9.925
5.841
4.604
4.032
3.078
1.886
1
0.816
3
6.314
2.920
2.353
2.132
2.015
15.894
4.849
3.482
2.999
2.757
636.619
31.599
12.924
8.610
6.869
1.963
1.386
12.706
4.303
3.182
2.776
2.571
31.821
127.321
14.089
7.453
5.598
4.773
318.309
22.327
10.215
7.173
5.893
1.000
1.376
2
1.061
6.965
0.765
0.741
0.727
1.250
1.190
4.541
3.747
3.365
0.978
1.638
0.941
0.920
1.533
1.476
1.156
2.447
2.365
1.134
1.943
1.895
1.860
1,833
2.612
2.517
3.143
2.998
2.896
2.821
2.764
4.317
4.029
3.833
3.690
5.208
4.785
4.501
4.297
5.959
0.718
6
0.711
0.906
0.896
0.889
0.883
3.707
3.499
3.355
3.250
3.169
1.440
1.119
1.108
1.100
7
1.415
1.397
1.383
1.372
5.408
2.306
2.262
2.228
8
0.706
2.449
5.041
9
0.703
2.398
4.781
10
0.700
0.879
1.093
1.812
2.359
3.581
4.144
4.587
2.201
2.179
2.160
2.145
2.131
3.106
3.055
3.012
2.977
2.947
3.497
3.428
3.372
3.326
3.286
4.025
3.930
3.852
3.787
3.733
4.437
4.318
11
1.088
1.363
1.356
1.350
1.345
1.341
2.328
2.303
2.282
2.264
2.249
2.718
2.681
2.650
2.624
2.602
0.697
0.876
1.796
0.873
0.870
12
1.083
0.695
0.694
1.782
13
1.079
1.771
4.221
0.692
0.691
0.868
0.866
14
1.076
1.761
1.753
4.140
15
1.074
4.073
1.337
1.333
1.330
1.328
1.325
1.746
1.740
1.734
1.729
1.725
2.120
2.110
2.101
2.093
2.086
2.235
2.224
2.214
2.205
3.252
3.222
3.197
3.174
3.153
3.686
3.646
3.610
3.579
16
0.690
0.865
0.863
0.862
1.071
2.583
2.567
2.552
2.539
2.528
2.921
1.069
1.067
1.066
1.064
2.898
2.878
2.861
2.845
4.015
3.965
3.922
3.883
3.850
17
0.689
0.688
0.688
0.687
18
19
0.861
0.860
20
2.197
3.552
0.686
0.686
0.685
0.859
0.858
0.858
0.857
0.856
1.721
1.717
1.714
1.711
1.708
3.527
3.505
3.485
3.467
3.450
1.063
1.061
2.080
2.074
2.069
2.064
2.060
2.189
2.183
3.135
3.119
3.104
3.091
3.078
21
1.323
2.518
2.831
3.819
1.321
1.319
1.318
1.316
2.508
2.500
2.492
2.485
2.819
2.807
2.797
2.787
22
3.792
1.060
1.059
1.058
23
2.177
24
25
2.172
2.167
3.768
3.745
3.725
0.685
0.684
0.684
0.684
0.683
0.683
0.683
0.856
0.855
0.855
0.854
0.854
2.056
2.052
2.048
2.045
2.042
2.779
2.771
2.763
2.756
2.750
3.707
3.690
3.674
3.659
3.646
1.058
1.315
1.706
1.703
1.701
1.699
1.697
2.162
2.158
2.154
2.150
2.147
2.479
2.473
2.467
2.462
2.457
3.067
3.057
3.047
3.038
3.030
3.435
3.421
3.408
3.396
3.385
26
1.057
27
28
29
30
1.314
1.313
1.055 1.311
1.055
1.056
1.310
0.682
0.682
0.682
0.853
0.853
0.853
1.054
1.054
1.053
1.052
1.052
1.309
1.309
1.308
1.307
1.306
1.696
1.694
1.692
1.691
1.690
2.744
2.738
2.733
2.728
2.724
31
2.040
2.144
2.453
2.449
2.445
2.441
2.438
3.022
32
33
34
35
2.037
2.035
2.032
2.030
2.141
2.138
2.136
2.133
3.375
3.365
3.356
3.348
3.633
3.622
3.611
3.601
3.591
3.015
3.008
0.852
0.852
3.002
2.996
0.682
0.682
3.340
0.852
0.851
0.851
1.052
1.051
1.051
1.050
1.050
1.306
1.305
1.304
1.304
1.303
2.028
2.026
2.024
2.719
2.715
2.712
36
0.681
0.681
0.681
0.681
1.688
2.131
2.434
2.431
2.429
2.990
2.985
2.980
2.976
2.971
3.333
3.326
3.319
3.313
3.307
3.582
3.574
3.566
3.558
3.551
37
38
1.687
2.129
1.686
1.685
1.684
2.127
2.125
2.123
39
0.851
2.023
2.426
2.708
40
0.681
0.851
2.021
2.423
2.704
1.047
1.045
0.679
0.679
0.678
0.678
1.676
1.671
1.667
1.664
0.849
1.299
1.296
2.403
2.390
2.381
2.374
2.937
2.915
2.899
2.887
3.496
3.460
3.435
3.416
50
2.009
2.109
2.678
2.660
2.648
2.639
3.261
3.232
3.211
3.195
60
2.000
1.994
1.990
2.099
2.093
2.088
0.848
0.847
0.846
70
1.044
1.043
1.294
80
1.292
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 63.657 9.925 5.841 4.604 4.032 3.078 1.886 1 0.816 3 6.314 2.920 2.353 2.132 2.015 15.894 4.849 3.482 2.999 2.757 636.619 31.599 12.924 8.610 6.869 1.963 1.386 12.706 4.303 3.182 2.776 2.571 31.821 127.321 14.089 7.453 5.598 4.773 318.309 22.327 10.215 7.173 5.893 1.000 1.376 2 1.061 6.965 0.765 0.741 0.727 1.250 1.190 4.541 3.747 3.365 0.978 1.638 0.941 0.920 1.533 1.476 1.156 2.447 2.365 1.134 1.943 1.895 1.860 1,833 2.612 2.517 3.143 2.998 2.896 2.821 2.764 4.317 4.029 3.833 3.690 5.208 4.785 4.501 4.297 5.959 0.718 6 0.711 0.906 0.896 0.889 0.883 3.707 3.499 3.355 3.250 3.169 1.440 1.119 1.108 1.100 7 1.415 1.397 1.383 1.372 5.408 2.306 2.262 2.228 8 0.706 2.449 5.041 9 0.703 2.398 4.781 10 0.700 0.879 1.093 1.812 2.359 3.581 4.144 4.587 2.201 2.179 2.160 2.145 2.131 3.106 3.055 3.012 2.977 2.947 3.497 3.428 3.372 3.326 3.286 4.025 3.930 3.852 3.787 3.733 4.437 4.318 11 1.088 1.363 1.356 1.350 1.345 1.341 2.328 2.303 2.282 2.264 2.249 2.718 2.681 2.650 2.624 2.602 0.697 0.876 1.796 0.873 0.870 12 1.083 0.695 0.694 1.782 13 1.079 1.771 4.221 0.692 0.691 0.868 0.866 14 1.076 1.761 1.753 4.140 15 1.074 4.073 1.337 1.333 1.330 1.328 1.325 1.746 1.740 1.734 1.729 1.725 2.120 2.110 2.101 2.093 2.086 2.235 2.224 2.214 2.205 3.252 3.222 3.197 3.174 3.153 3.686 3.646 3.610 3.579 16 0.690 0.865 0.863 0.862 1.071 2.583 2.567 2.552 2.539 2.528 2.921 1.069 1.067 1.066 1.064 2.898 2.878 2.861 2.845 4.015 3.965 3.922 3.883 3.850 17 0.689 0.688 0.688 0.687 18 19 0.861 0.860 20 2.197 3.552 0.686 0.686 0.685 0.859 0.858 0.858 0.857 0.856 1.721 1.717 1.714 1.711 1.708 3.527 3.505 3.485 3.467 3.450 1.063 1.061 2.080 2.074 2.069 2.064 2.060 2.189 2.183 3.135 3.119 3.104 3.091 3.078 21 1.323 2.518 2.831 3.819 1.321 1.319 1.318 1.316 2.508 2.500 2.492 2.485 2.819 2.807 2.797 2.787 22 3.792 1.060 1.059 1.058 23 2.177 24 25 2.172 2.167 3.768 3.745 3.725 0.685 0.684 0.684 0.684 0.683 0.683 0.683 0.856 0.855 0.855 0.854 0.854 2.056 2.052 2.048 2.045 2.042 2.779 2.771 2.763 2.756 2.750 3.707 3.690 3.674 3.659 3.646 1.058 1.315 1.706 1.703 1.701 1.699 1.697 2.162 2.158 2.154 2.150 2.147 2.479 2.473 2.467 2.462 2.457 3.067 3.057 3.047 3.038 3.030 3.435 3.421 3.408 3.396 3.385 26 1.057 27 28 29 30 1.314 1.313 1.055 1.311 1.055 1.056 1.310 0.682 0.682 0.682 0.853 0.853 0.853 1.054 1.054 1.053 1.052 1.052 1.309 1.309 1.308 1.307 1.306 1.696 1.694 1.692 1.691 1.690 2.744 2.738 2.733 2.728 2.724 31 2.040 2.144 2.453 2.449 2.445 2.441 2.438 3.022 32 33 34 35 2.037 2.035 2.032 2.030 2.141 2.138 2.136 2.133 3.375 3.365 3.356 3.348 3.633 3.622 3.611 3.601 3.591 3.015 3.008 0.852 0.852 3.002 2.996 0.682 0.682 3.340 0.852 0.851 0.851 1.052 1.051 1.051 1.050 1.050 1.306 1.305 1.304 1.304 1.303 2.028 2.026 2.024 2.719 2.715 2.712 36 0.681 0.681 0.681 0.681 1.688 2.131 2.434 2.431 2.429 2.990 2.985 2.980 2.976 2.971 3.333 3.326 3.319 3.313 3.307 3.582 3.574 3.566 3.558 3.551 37 38 1.687 2.129 1.686 1.685 1.684 2.127 2.125 2.123 39 0.851 2.023 2.426 2.708 40 0.681 0.851 2.021 2.423 2.704 1.047 1.045 0.679 0.679 0.678 0.678 1.676 1.671 1.667 1.664 0.849 1.299 1.296 2.403 2.390 2.381 2.374 2.937 2.915 2.899 2.887 3.496 3.460 3.435 3.416 50 2.009 2.109 2.678 2.660 2.648 2.639 3.261 3.232 3.211 3.195 60 2.000 1.994 1.990 2.099 2.093 2.088 0.848 0.847 0.846 70 1.044 1.043 1.294 80 1.292
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