Critical Values of the t-Distribution (page 1) a v 0.40 0.30 0.20 0.15 0.10 0.05 0.025 1 0.325 0.727 1.376 1.963 3.078 6.314 12.706 2 0.289 0.617 1.061 1.386 1.886 2.920 4.303 3 0.277 0.584 0.978 1.250 1.638 2.353 3.182 4 0.271 0.569 0.941 1.190 1.533 2.132 2.776 5 0.267 0.559 0.920 1.156 1.476 2.015 2.571 6 0.265 0.553 0.906 1.134 1.440 1.943 2.447 7 0.263 0.549 0.896 1.119 1.415 1.895 2.365 8 0.262 0.546 0.889 1.108 1.397 1.860 2.306 9 0.261 0.543 0.883 1.100 1.383 1.833 2.262 10 0.260 0.542 0.879 1.093 1.372 1.812 2.228 11 0.260 0.540 0.876 1.088 1.363 1.796 2.201 40 120 2222222222234828 0.259 0.539 0.873 1.083 1.356 1.782 2.179 13 0.259 0.538 0.870 1.079 1.350 1.771 2.160 0.258 0.537 0.868 1.076 1.345 1.761 2.145 0.258 0.536 0.866 1.074 1.341 1.753 2.131 16 0.258 0.535 0.865 1.071 1.337 1.746 2.120 0.257 0.534 0.863 1.069 1.333 1.740 2.110 0.257 0.534 0.862 1.067 1.330 1.734 2.101 0.257 0.533 0.861 1.066 1.328 1.729 2.093 20 0.257 0.533 0.860 1.064 1.325 1.725 2.086 21 0.257 0.532 0.859 1.063 1.323 1.721 2.080 0.256 0.532 0.858 1.061 1.321 1.717 2.074 0.256 0.532 0.858 1.060 1.319 1.714 2.069 0.256 0.531 0.857 1.059 1.318 1.711 2.064 25 0.256 0.531 0.856 1.058 1.316 1.708 2.060 26 0.256 0.531 0.856 1.058 1.315 1.706 2.056 27 0.256 0.531 0.855 1.057 1.314 1.703 2.052 0.256 0.530 0.855 1.056 1.313 1.701 2.048 29 0.256 0.530 0.854 1.055 1.311 1.699 2.045 30 0.256 0.530 0.854 1.055 1.310 1.697 2.042 0.255 0.529 0.851 1.050 1.303 1.684 2.021 60 0.254 0.527 0.848 1.045 1.296 1.671 2.000 0.254 0.526 0.845 1.041 1.289 1.658 1.980 0.253 0.524 0.842 1.036 1.282 1.645 1.960 e v 0.40 0.30 0.20 0.15 0.10 0.05 0.025 ¡A a Dr > > > с - 2 < > C + Critical Values of the t-Distribution (page 2) a 0.02 0.015 0.01 0.0075 0.005 0.0025 0.0005 1 15.894 21.205 31.821 42.433 63.656 127.321 636.578 2 4.849 5.643 6.965 8.073 9.925 14.089 31.600 3 3.482 3.896 4.541 5.047 5.841 7.453 12.924 4 2.999 3.298 3.747 4.088 4.604 5.598 8.610 5 2.757 3.003 3.365 3.634 4.032 4.773 6.869 6 2.612 2.829 3.143 3.372 3.707 4.317 5.959 7 2.517 2.715 2.998 3.203 3.499 4.029 5.408 8 2.449 2.634 2.896 3.085 3.355 3.833 5.041 2.398 2.574 2.821 2.998 3.250 3.690 4.781 2.359 2.527 2.764 2.932 3.169 3.581 4.587 2.328 2.491 2.718 2.879 3.106 3.497 4.437 2.303 2.461 2.681 2.836 3.055 3.428 4.318 2.282 2.436 2.650 2.801 3.012 3.372 4.221 2.264 2.415 2.624 2.771 2.977 3.326 4.140 2.249 2.397 2.602 2.746 2.947 3.286 4.073 2.235 2.382 2.583 2.724 2.921 3.252 4.015 2.224 2.368 2.567 2.706 2.898 3.222 3.965 2.214 2.356 2.552 2.689 2.878 3.197 3.922 120 2 2 2 2 9 8 285 2.205 2.346 2.539 2.674 2.861 3.174 3.883 2.197 2.336 2.528 2.661 2.845 3.153 3.850 2.189 2.328 2.518 2.649 2.831 3.135 3.819 2.183 2.320 2.508 2.639 2.819 3.119 3.792 2.177 2.313 2.500 2.629 2.807 3.104 3.768 24 2.172 2.307 2.492 2.620 2.797 3.091 3.745 2.167 2.301 2.485 2.612 2.787 3.078 3.725 2.162 2.296 2.479 2.605 2.779 3.067 3.707 2.158 2.291 2.473 2.598 2.771 3.057 3.689 28 2.154 2.286 2.467 2.592 2.763 3.047 3.674 29 2.150 2.282 2.462 2.586 2.756 3.038 3.660 30 2.147 2.278 2.457 2.581 2.750 3.030 3.646 40 2.123 2.250 2.423 2.542 2.704 2.971 3.551 60 2.099 2.223 2.390 2.504 2.660 2.915 3.460 2.076 2.196 2.358 2.468 2.617 2.860 3.373 2.054 2.170 2.326 2.432 2.576 2.807 3.290 0.02 0.015 0.01 0.0075 0.005 0.0025 0.0005 a Chemical compound data x (°C) y (grams) 0 7 5 7 fitted linear regression equation 15 12 15 14 30 21 24 26 45 44 42 41 60 48 53 47 75 52 56 58 y = 5.3016 +0.7060x $² = 13.93 x=37.5 Sxx = 11812.50
Critical Values of the t-Distribution (page 1) a v 0.40 0.30 0.20 0.15 0.10 0.05 0.025 1 0.325 0.727 1.376 1.963 3.078 6.314 12.706 2 0.289 0.617 1.061 1.386 1.886 2.920 4.303 3 0.277 0.584 0.978 1.250 1.638 2.353 3.182 4 0.271 0.569 0.941 1.190 1.533 2.132 2.776 5 0.267 0.559 0.920 1.156 1.476 2.015 2.571 6 0.265 0.553 0.906 1.134 1.440 1.943 2.447 7 0.263 0.549 0.896 1.119 1.415 1.895 2.365 8 0.262 0.546 0.889 1.108 1.397 1.860 2.306 9 0.261 0.543 0.883 1.100 1.383 1.833 2.262 10 0.260 0.542 0.879 1.093 1.372 1.812 2.228 11 0.260 0.540 0.876 1.088 1.363 1.796 2.201 40 120 2222222222234828 0.259 0.539 0.873 1.083 1.356 1.782 2.179 13 0.259 0.538 0.870 1.079 1.350 1.771 2.160 0.258 0.537 0.868 1.076 1.345 1.761 2.145 0.258 0.536 0.866 1.074 1.341 1.753 2.131 16 0.258 0.535 0.865 1.071 1.337 1.746 2.120 0.257 0.534 0.863 1.069 1.333 1.740 2.110 0.257 0.534 0.862 1.067 1.330 1.734 2.101 0.257 0.533 0.861 1.066 1.328 1.729 2.093 20 0.257 0.533 0.860 1.064 1.325 1.725 2.086 21 0.257 0.532 0.859 1.063 1.323 1.721 2.080 0.256 0.532 0.858 1.061 1.321 1.717 2.074 0.256 0.532 0.858 1.060 1.319 1.714 2.069 0.256 0.531 0.857 1.059 1.318 1.711 2.064 25 0.256 0.531 0.856 1.058 1.316 1.708 2.060 26 0.256 0.531 0.856 1.058 1.315 1.706 2.056 27 0.256 0.531 0.855 1.057 1.314 1.703 2.052 0.256 0.530 0.855 1.056 1.313 1.701 2.048 29 0.256 0.530 0.854 1.055 1.311 1.699 2.045 30 0.256 0.530 0.854 1.055 1.310 1.697 2.042 0.255 0.529 0.851 1.050 1.303 1.684 2.021 60 0.254 0.527 0.848 1.045 1.296 1.671 2.000 0.254 0.526 0.845 1.041 1.289 1.658 1.980 0.253 0.524 0.842 1.036 1.282 1.645 1.960 e v 0.40 0.30 0.20 0.15 0.10 0.05 0.025 ¡A a Dr > > > с - 2 < > C + Critical Values of the t-Distribution (page 2) a 0.02 0.015 0.01 0.0075 0.005 0.0025 0.0005 1 15.894 21.205 31.821 42.433 63.656 127.321 636.578 2 4.849 5.643 6.965 8.073 9.925 14.089 31.600 3 3.482 3.896 4.541 5.047 5.841 7.453 12.924 4 2.999 3.298 3.747 4.088 4.604 5.598 8.610 5 2.757 3.003 3.365 3.634 4.032 4.773 6.869 6 2.612 2.829 3.143 3.372 3.707 4.317 5.959 7 2.517 2.715 2.998 3.203 3.499 4.029 5.408 8 2.449 2.634 2.896 3.085 3.355 3.833 5.041 2.398 2.574 2.821 2.998 3.250 3.690 4.781 2.359 2.527 2.764 2.932 3.169 3.581 4.587 2.328 2.491 2.718 2.879 3.106 3.497 4.437 2.303 2.461 2.681 2.836 3.055 3.428 4.318 2.282 2.436 2.650 2.801 3.012 3.372 4.221 2.264 2.415 2.624 2.771 2.977 3.326 4.140 2.249 2.397 2.602 2.746 2.947 3.286 4.073 2.235 2.382 2.583 2.724 2.921 3.252 4.015 2.224 2.368 2.567 2.706 2.898 3.222 3.965 2.214 2.356 2.552 2.689 2.878 3.197 3.922 120 2 2 2 2 9 8 285 2.205 2.346 2.539 2.674 2.861 3.174 3.883 2.197 2.336 2.528 2.661 2.845 3.153 3.850 2.189 2.328 2.518 2.649 2.831 3.135 3.819 2.183 2.320 2.508 2.639 2.819 3.119 3.792 2.177 2.313 2.500 2.629 2.807 3.104 3.768 24 2.172 2.307 2.492 2.620 2.797 3.091 3.745 2.167 2.301 2.485 2.612 2.787 3.078 3.725 2.162 2.296 2.479 2.605 2.779 3.067 3.707 2.158 2.291 2.473 2.598 2.771 3.057 3.689 28 2.154 2.286 2.467 2.592 2.763 3.047 3.674 29 2.150 2.282 2.462 2.586 2.756 3.038 3.660 30 2.147 2.278 2.457 2.581 2.750 3.030 3.646 40 2.123 2.250 2.423 2.542 2.704 2.971 3.551 60 2.099 2.223 2.390 2.504 2.660 2.915 3.460 2.076 2.196 2.358 2.468 2.617 2.860 3.373 2.054 2.170 2.326 2.432 2.576 2.807 3.290 0.02 0.015 0.01 0.0075 0.005 0.0025 0.0005 a Chemical compound data x (°C) y (grams) 0 7 5 7 fitted linear regression equation 15 12 15 14 30 21 24 26 45 44 42 41 60 48 53 47 75 52 56 58 y = 5.3016 +0.7060x $² = 13.93 x=37.5 Sxx = 11812.50
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 15E: Describe the standard normal distribution. What are its characteristics?
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 and b.
a) Construct a 99% confidence interval for the average amount of chemical that will dissolve in 100 grams of water at 50°C.
______ < μ_y|50 < _______ (Round to three decimal places as needed.)
b) Construct a 99% prediction interval for the amount of chemical that will dissolve in 100 grams of water at
50°C.
__________ < y₀ < _____________ (Round to three decimal places as needed.)
Transcribed Image Text:Critical Values of the t-Distribution (page 1)
a
v
0.40
0.30
0.20
0.15
0.10
0.05
0.025
1
0.325
0.727
1.376
1.963
3.078
6.314
12.706
2
0.289
0.617
1.061
1.386
1.886
2.920
4.303
3
0.277
0.584
0.978
1.250
1.638
2.353
3.182
4
0.271
0.569
0.941
1.190
1.533
2.132
2.776
5
0.267
0.559
0.920
1.156
1.476
2.015
2.571
6
0.265
0.553
0.906
1.134
1.440
1.943
2.447
7
0.263
0.549
0.896
1.119
1.415
1.895
2.365
8
0.262
0.546
0.889
1.108
1.397
1.860
2.306
9
0.261
0.543
0.883
1.100
1.383
1.833
2.262
10
0.260
0.542
0.879
1.093
1.372
1.812
2.228
11
0.260
0.540
0.876
1.088
1.363
1.796
2.201
40
120
2222222222234828
0.259
0.539
0.873
1.083
1.356
1.782
2.179
13
0.259
0.538
0.870
1.079
1.350
1.771
2.160
0.258
0.537
0.868
1.076
1.345
1.761
2.145
0.258
0.536
0.866
1.074
1.341
1.753
2.131
16
0.258
0.535
0.865
1.071
1.337
1.746
2.120
0.257
0.534
0.863
1.069
1.333
1.740
2.110
0.257
0.534
0.862
1.067
1.330
1.734
2.101
0.257
0.533
0.861
1.066
1.328
1.729
2.093
20
0.257
0.533
0.860
1.064
1.325
1.725
2.086
21
0.257
0.532
0.859
1.063
1.323
1.721
2.080
0.256
0.532
0.858
1.061
1.321
1.717
2.074
0.256
0.532
0.858
1.060
1.319
1.714
2.069
0.256
0.531
0.857
1.059
1.318
1.711
2.064
25
0.256
0.531
0.856
1.058
1.316
1.708
2.060
26
0.256
0.531
0.856
1.058
1.315
1.706
2.056
27
0.256
0.531
0.855
1.057
1.314
1.703
2.052
0.256
0.530
0.855
1.056
1.313
1.701
2.048
29
0.256
0.530
0.854
1.055
1.311
1.699
2.045
30
0.256
0.530
0.854
1.055
1.310
1.697
2.042
0.255
0.529
0.851
1.050
1.303
1.684
2.021
60
0.254
0.527
0.848
1.045
1.296
1.671
2.000
0.254
0.526
0.845
1.041
1.289
1.658
1.980
0.253
0.524
0.842
1.036
1.282
1.645
1.960
e
v
0.40
0.30
0.20
0.15
0.10
0.05
0.025
¡A
a
Dr
> > >
с
- 2 < > C +
Critical Values of the t-Distribution (page 2)
a
0.02
0.015
0.01
0.0075
0.005
0.0025
0.0005
1
15.894
21.205
31.821
42.433
63.656
127.321
636.578
2
4.849
5.643
6.965
8.073
9.925
14.089
31.600
3
3.482
3.896
4.541
5.047
5.841
7.453
12.924
4
2.999
3.298
3.747
4.088
4.604
5.598
8.610
5
2.757
3.003
3.365
3.634
4.032
4.773
6.869
6
2.612
2.829
3.143
3.372
3.707
4.317
5.959
7
2.517
2.715
2.998
3.203
3.499
4.029
5.408
8
2.449
2.634
2.896
3.085
3.355
3.833
5.041
2.398
2.574
2.821
2.998
3.250
3.690
4.781
2.359
2.527
2.764
2.932
3.169
3.581
4.587
2.328
2.491
2.718
2.879
3.106
3.497
4.437
2.303
2.461
2.681
2.836
3.055
3.428
4.318
2.282
2.436
2.650
2.801
3.012
3.372
4.221
2.264
2.415
2.624
2.771
2.977
3.326
4.140
2.249
2.397
2.602
2.746
2.947
3.286
4.073
2.235
2.382
2.583
2.724
2.921
3.252
4.015
2.224
2.368
2.567
2.706
2.898
3.222
3.965
2.214
2.356
2.552
2.689
2.878
3.197
3.922
120
2 2 2 2 9 8 285
2.205
2.346
2.539
2.674
2.861
3.174
3.883
2.197
2.336
2.528
2.661
2.845
3.153
3.850
2.189
2.328
2.518
2.649
2.831
3.135
3.819
2.183
2.320
2.508
2.639
2.819
3.119
3.792
2.177
2.313
2.500
2.629
2.807
3.104
3.768
24
2.172
2.307
2.492
2.620
2.797
3.091
3.745
2.167
2.301
2.485
2.612
2.787
3.078
3.725
2.162
2.296
2.479
2.605
2.779
3.067
3.707
2.158
2.291
2.473
2.598
2.771
3.057
3.689
28
2.154
2.286
2.467
2.592
2.763
3.047
3.674
29
2.150
2.282
2.462
2.586
2.756
3.038
3.660
30
2.147
2.278
2.457
2.581
2.750
3.030
3.646
40
2.123
2.250
2.423
2.542
2.704
2.971
3.551
60
2.099
2.223
2.390
2.504
2.660
2.915
3.460
2.076
2.196
2.358
2.468
2.617
2.860
3.373
2.054
2.170
2.326
2.432
2.576
2.807
3.290
0.02
0.015
0.01
0.0075
0.005
0.0025
0.0005
a
Transcribed Image Text:Chemical compound data
x (°C)
y (grams)
0
7
5
7
fitted linear regression equation
15
12
15
14
30
21
24
26
45
44
42
41
60
48
53
47
75
52
56
58
y = 5.3016 +0.7060x
$² = 13.93
x=37.5
Sxx = 11812.50
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