Critical Values of the t-Distribution Critical Values of the t-Distribution a ☐ = a บ 0.02 0.015 0.01 0.0075 0.005 0.0025 0.0005 ข 0.40 0.30 0.20 0.15 0.10 0.05 0.025 1 15.895 21.205 31.821 42.433 63.657 127.321 636.619 1 0.325 0.727 1.376 1.963 3.078 6.314 12.706 2 4.849 5.643 6.965 8.073 9.925 14.089 31.599 2 0.289 0.617 1.061 1.386 1.886 2.920 4.303 3 3.482 3.896 4.541 5.047 5.841 7.453 12.924 3 0.277 0.584 0.978 1.250 1.638 2.353 3.182 4 2.999 3.298 3.747 4.088 4.604 5.598 8.610 4 0.271 0.569 0.941 1.190 1.533 2.132 2.776 5 2.757 3.003 3.365 3.634 4.032 4.773 6.869 5 0.267 0.559 0.920 1.156 1.476 2.015 2.571 6 2.612 2.829 3.143 3.372 3.707 4.317 5.959 6 0.265 0.553 0.906 1.134 1.440 1.943 2.447 7 2.517 2.715 2.998 3.203 3.499 4.029 5.408 7 0.263 0.549 0.896 1.119 1.415 1.895 2.365 8 2.449 2.634 2.896 3.085 3.355 3.833 5.041 8 0.262 0.546 0.889 1.108 1.397 1.860 2.306 9 2.398 2.574 2.821 2.998 3.250 3.690 4.781 9 0.261 0.543 0.883 1.100 1.383 1.833 2.262 10 2.359 2.527 2.764 2.932 3.169 3.581 4.587 10 0.260 0.542 0.879 1.093 1.372 1.812 2.228 11 2.328 2.491 2.718 2.879 3.106 3.497 4.437 0.260 0.540 0.876 1.088 1.363 1.796 2.201 12 2.303 2.461 2.681 2.836 3.055 3.428 4.318 0.259 0.539 0.873 1.083 1.356 1.782 2.179 13 2.282 2.436 2.650 2.801 3.012 3.372 4.221 0.259 0.538 0.870 1.079 1.350 1.771 2.160 14 2.264 2.415 2.624 2.771 2.977 3.326 4.140 0.258 0.537 0.868 1.076 1.345 1.761 2.145 15 2.249 2.397 2.602 2.746 2.947 3.286 4.073 0.258 0.536 0.866 1.074 1.341 1.753 2.131 16 2.235 2.382 2.583 2.724 2.921 3.252 4.015 0.258 0.535 0.865 1.071 1.337 1.746 2.120 17 2.224 2.368 2.567 2.706 2.898 3.222 3.965 0.257 0.534 0.863 1.069 1.333 1.740 2.110 18 2.214 2.356 2.552 2.689 2.878 3.197 3.922 0.257 0.534 0.862 1.067 1.330 1.734 2.101 19 2.205 2.346 2.539 2.674 2.861 3.174 3.883 120 22 223 222988 0.257 0.533 0.861 1.066 1.328 1.729 2.093 20 2.197 2.336 2.528 2.661 2.845 3.153 3.850 0.257 0.533 0.860 1.064 1.325 1.725 2.086 21 2.189 2.328 2.518 2.649 2.831 3.135 3.819 0.257 0.532 0.859 1.063 1.323 1.721 2.080 22 2.183 2.320 2.508 2.639 2.819 3.119 3.792 0.256 0.532 0.858 1.061 1.321 1.717 2.074 23 2.177 2.313 2.500 2.629 2.807 3.104 3.768 0.256 0.532 0.858 1.060 1.319 1.714 2.069 24 2.172 2.307 2.492 2.620 2.797 3.091 3.745 0.256 0.531 0.857 1.059 1.318 1.711 2.064 25 2.167 2.301 2.485 2.612 2.787 3.078 3.725 0.256 0.531 0.856 1.058 1.316 1.708 2.060 26 2.162 2.296 2.479 2.605 2.779 3.067 3.707 0.256 0.531 0.856 1.058 1.315 1.706 2.056 27 2.158 2.291 2.473 2.598 2.771 3.057 3.690 0.256 0.531 0.855 1.057 1.314 1.703 2.052 1 28 2.154 2.286 2.467 2.592 2.763 3.047 3.674 0.256 0.530 0.855 1.056 1.313 1.701 2.048 29 2.150 2.282 2.462 2.586 2.756 3.038 3.659 0.256 0.530 0.854 1.055 1.311 1.699 2.045 30 2.147 2.278 2.457 2.581 2.750 3.030 3.646 0.256 0.530 0.854 1.055 1.310 1.697 2.042 40 2.123 2.250 2.423 2.542 2.704 2.971 3.551 0.255 0.529 0.851 1.050 1.303 1.684 2.021 60 2.099 2.223 2.390 2.504 2.660 2.915 3.460 0.254 0.527 0.848 1.045 1.296 1.671 2.000 120 2.076 2.196 2.358 2.468 2.617 2.860 3.373 0.254 0.526 0.845 1.041 1.289 1.658 1.980 ∞ 2.054 2.170 2.326 2.432 2.576 2.807 3.291 0.253 0.524 0.842 1.036 1.282 1.645 1.960 国 Chemical compound data x (°C) y (grams) 0 8 6 8 53462 15 13 12 15 fitted linear regression equation 30 21 23 25 ŷ = 5.6508 +0.6775x 39 42 38 60 53 50 46 75 55 54 51
Critical Values of the t-Distribution Critical Values of the t-Distribution a ☐ = a บ 0.02 0.015 0.01 0.0075 0.005 0.0025 0.0005 ข 0.40 0.30 0.20 0.15 0.10 0.05 0.025 1 15.895 21.205 31.821 42.433 63.657 127.321 636.619 1 0.325 0.727 1.376 1.963 3.078 6.314 12.706 2 4.849 5.643 6.965 8.073 9.925 14.089 31.599 2 0.289 0.617 1.061 1.386 1.886 2.920 4.303 3 3.482 3.896 4.541 5.047 5.841 7.453 12.924 3 0.277 0.584 0.978 1.250 1.638 2.353 3.182 4 2.999 3.298 3.747 4.088 4.604 5.598 8.610 4 0.271 0.569 0.941 1.190 1.533 2.132 2.776 5 2.757 3.003 3.365 3.634 4.032 4.773 6.869 5 0.267 0.559 0.920 1.156 1.476 2.015 2.571 6 2.612 2.829 3.143 3.372 3.707 4.317 5.959 6 0.265 0.553 0.906 1.134 1.440 1.943 2.447 7 2.517 2.715 2.998 3.203 3.499 4.029 5.408 7 0.263 0.549 0.896 1.119 1.415 1.895 2.365 8 2.449 2.634 2.896 3.085 3.355 3.833 5.041 8 0.262 0.546 0.889 1.108 1.397 1.860 2.306 9 2.398 2.574 2.821 2.998 3.250 3.690 4.781 9 0.261 0.543 0.883 1.100 1.383 1.833 2.262 10 2.359 2.527 2.764 2.932 3.169 3.581 4.587 10 0.260 0.542 0.879 1.093 1.372 1.812 2.228 11 2.328 2.491 2.718 2.879 3.106 3.497 4.437 0.260 0.540 0.876 1.088 1.363 1.796 2.201 12 2.303 2.461 2.681 2.836 3.055 3.428 4.318 0.259 0.539 0.873 1.083 1.356 1.782 2.179 13 2.282 2.436 2.650 2.801 3.012 3.372 4.221 0.259 0.538 0.870 1.079 1.350 1.771 2.160 14 2.264 2.415 2.624 2.771 2.977 3.326 4.140 0.258 0.537 0.868 1.076 1.345 1.761 2.145 15 2.249 2.397 2.602 2.746 2.947 3.286 4.073 0.258 0.536 0.866 1.074 1.341 1.753 2.131 16 2.235 2.382 2.583 2.724 2.921 3.252 4.015 0.258 0.535 0.865 1.071 1.337 1.746 2.120 17 2.224 2.368 2.567 2.706 2.898 3.222 3.965 0.257 0.534 0.863 1.069 1.333 1.740 2.110 18 2.214 2.356 2.552 2.689 2.878 3.197 3.922 0.257 0.534 0.862 1.067 1.330 1.734 2.101 19 2.205 2.346 2.539 2.674 2.861 3.174 3.883 120 22 223 222988 0.257 0.533 0.861 1.066 1.328 1.729 2.093 20 2.197 2.336 2.528 2.661 2.845 3.153 3.850 0.257 0.533 0.860 1.064 1.325 1.725 2.086 21 2.189 2.328 2.518 2.649 2.831 3.135 3.819 0.257 0.532 0.859 1.063 1.323 1.721 2.080 22 2.183 2.320 2.508 2.639 2.819 3.119 3.792 0.256 0.532 0.858 1.061 1.321 1.717 2.074 23 2.177 2.313 2.500 2.629 2.807 3.104 3.768 0.256 0.532 0.858 1.060 1.319 1.714 2.069 24 2.172 2.307 2.492 2.620 2.797 3.091 3.745 0.256 0.531 0.857 1.059 1.318 1.711 2.064 25 2.167 2.301 2.485 2.612 2.787 3.078 3.725 0.256 0.531 0.856 1.058 1.316 1.708 2.060 26 2.162 2.296 2.479 2.605 2.779 3.067 3.707 0.256 0.531 0.856 1.058 1.315 1.706 2.056 27 2.158 2.291 2.473 2.598 2.771 3.057 3.690 0.256 0.531 0.855 1.057 1.314 1.703 2.052 1 28 2.154 2.286 2.467 2.592 2.763 3.047 3.674 0.256 0.530 0.855 1.056 1.313 1.701 2.048 29 2.150 2.282 2.462 2.586 2.756 3.038 3.659 0.256 0.530 0.854 1.055 1.311 1.699 2.045 30 2.147 2.278 2.457 2.581 2.750 3.030 3.646 0.256 0.530 0.854 1.055 1.310 1.697 2.042 40 2.123 2.250 2.423 2.542 2.704 2.971 3.551 0.255 0.529 0.851 1.050 1.303 1.684 2.021 60 2.099 2.223 2.390 2.504 2.660 2.915 3.460 0.254 0.527 0.848 1.045 1.296 1.671 2.000 120 2.076 2.196 2.358 2.468 2.617 2.860 3.373 0.254 0.526 0.845 1.041 1.289 1.658 1.980 ∞ 2.054 2.170 2.326 2.432 2.576 2.807 3.291 0.253 0.524 0.842 1.036 1.282 1.645 1.960 国 Chemical compound data x (°C) y (grams) 0 8 6 8 53462 15 13 12 15 fitted linear regression equation 30 21 23 25 ŷ = 5.6508 +0.6775x 39 42 38 60 53 50 46 75 55 54 51
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
The amounts of a chemical compound y that dissolved in 100 grams of water at various temperatures x were recorded. The data were coded and recorded in the accompanying table. Use this information to answer parts a through c.
a) Evaluate s^2.
s^2 = _____ (Round to two decimal places as needed.)
b) Construct a 99% confidence interval for beta 0
_______ < beta 0 < _______(Round to three decimal places as needed.)
c) Construct a 99% confidence interval for beta 1
________ < beta 1 < _________ (Round to three decimal places as needed.)
Transcribed Image Text:Critical Values of the t-Distribution
Critical Values of the t-Distribution
a
☐ =
a
บ
0.02
0.015
0.01
0.0075
0.005
0.0025
0.0005
ข
0.40
0.30
0.20
0.15
0.10
0.05
0.025
1
15.895
21.205
31.821
42.433
63.657
127.321
636.619
1
0.325
0.727
1.376
1.963
3.078
6.314
12.706
2
4.849
5.643
6.965
8.073
9.925
14.089
31.599
2
0.289
0.617
1.061
1.386
1.886
2.920
4.303
3
3.482
3.896
4.541
5.047
5.841
7.453
12.924
3
0.277
0.584
0.978
1.250
1.638
2.353
3.182
4
2.999
3.298
3.747
4.088
4.604
5.598
8.610
4
0.271
0.569
0.941
1.190
1.533
2.132
2.776
5
2.757
3.003
3.365
3.634
4.032
4.773
6.869
5
0.267
0.559
0.920
1.156
1.476
2.015
2.571
6
2.612
2.829
3.143
3.372
3.707
4.317
5.959
6
0.265
0.553
0.906
1.134
1.440
1.943
2.447
7
2.517
2.715
2.998
3.203
3.499
4.029
5.408
7
0.263
0.549
0.896
1.119
1.415
1.895
2.365
8
2.449
2.634
2.896
3.085
3.355
3.833
5.041
8
0.262
0.546
0.889
1.108
1.397
1.860
2.306
9
2.398
2.574
2.821
2.998
3.250
3.690
4.781
9
0.261
0.543
0.883
1.100
1.383
1.833
2.262
10
2.359
2.527
2.764
2.932
3.169
3.581
4.587
10
0.260
0.542
0.879
1.093
1.372
1.812
2.228
11
2.328
2.491
2.718
2.879
3.106
3.497
4.437
0.260
0.540
0.876
1.088
1.363
1.796
2.201
12
2.303
2.461
2.681
2.836
3.055
3.428
4.318
0.259
0.539
0.873
1.083
1.356
1.782
2.179
13
2.282
2.436
2.650
2.801
3.012
3.372
4.221
0.259
0.538
0.870
1.079
1.350
1.771
2.160
14
2.264
2.415
2.624
2.771
2.977
3.326
4.140
0.258
0.537
0.868
1.076
1.345
1.761
2.145
15
2.249
2.397
2.602
2.746
2.947
3.286
4.073
0.258
0.536
0.866
1.074
1.341
1.753
2.131
16
2.235
2.382
2.583
2.724
2.921
3.252
4.015
0.258
0.535
0.865
1.071
1.337
1.746
2.120
17
2.224
2.368
2.567
2.706
2.898
3.222
3.965
0.257
0.534
0.863
1.069
1.333
1.740
2.110
18
2.214
2.356
2.552
2.689
2.878
3.197
3.922
0.257
0.534
0.862
1.067
1.330
1.734
2.101
19
2.205
2.346
2.539
2.674
2.861
3.174
3.883
120
22 223 222988
0.257
0.533
0.861
1.066
1.328
1.729
2.093
20
2.197
2.336
2.528
2.661
2.845
3.153
3.850
0.257
0.533
0.860
1.064
1.325
1.725
2.086
21
2.189
2.328
2.518
2.649
2.831
3.135
3.819
0.257
0.532
0.859
1.063
1.323
1.721
2.080
22
2.183
2.320
2.508
2.639
2.819
3.119
3.792
0.256
0.532
0.858
1.061
1.321
1.717
2.074
23
2.177
2.313
2.500
2.629
2.807
3.104
3.768
0.256
0.532
0.858
1.060
1.319
1.714
2.069
24
2.172
2.307
2.492
2.620
2.797
3.091
3.745
0.256
0.531
0.857
1.059
1.318
1.711
2.064
25
2.167
2.301
2.485
2.612
2.787
3.078
3.725
0.256
0.531
0.856
1.058
1.316
1.708
2.060
26
2.162
2.296
2.479
2.605
2.779
3.067
3.707
0.256
0.531
0.856
1.058
1.315
1.706
2.056
27
2.158
2.291
2.473
2.598
2.771
3.057
3.690
0.256
0.531
0.855
1.057
1.314
1.703
2.052
1
28
2.154
2.286
2.467
2.592
2.763
3.047
3.674
0.256
0.530
0.855
1.056
1.313
1.701
2.048
29
2.150
2.282
2.462
2.586
2.756
3.038
3.659
0.256
0.530
0.854
1.055
1.311
1.699
2.045
30
2.147
2.278
2.457
2.581
2.750
3.030
3.646
0.256
0.530
0.854
1.055
1.310
1.697
2.042
40
2.123
2.250
2.423
2.542
2.704
2.971
3.551
0.255
0.529
0.851
1.050
1.303
1.684
2.021
60
2.099
2.223
2.390
2.504
2.660
2.915
3.460
0.254
0.527
0.848
1.045
1.296
1.671
2.000
120
2.076
2.196
2.358
2.468
2.617
2.860
3.373
0.254
0.526
0.845
1.041
1.289
1.658
1.980
∞
2.054
2.170
2.326
2.432
2.576
2.807
3.291
0.253
0.524
0.842
1.036
1.282
1.645
1.960
国
Transcribed Image Text:Chemical compound data
x (°C)
y (grams)
0
8
6
8
53462
15
13
12
15
fitted linear regression equation
30
21
23
25
ŷ = 5.6508 +0.6775x
39
42
38
60
53
50
46
75
55
54
51
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