Sample opticalDens lot run westernBlot 1 1.053 A A 1.708 A A 2.99 0.977 A A 1.67 4 0.881 AB 1.47 0.788 A B 2.25 6 0.788 A B 0.15 7 0.896 AC 1.41 1.038 AC 2.51 9 0.963 AC 1.85 10 0.971 A D 1.7 11 1.234 AD 1.49 12 1.089 A D 1.92 13 0.984 A E 0.96 14 0.986 A E 1.64 15 1.067 A E 16 0.996 BA 1.77 17 1.129 BA 1.69 18 1.016 BA 3.01 19 1.019 B B 1.03 20 1.088 B B 1.94 21 1.28 BB 2.1 22 1.12 BC 0.83 23 1.054 BC 2.52 24 1.235 BC 1.78 1.327 BD 2.2 26 1.361 BD 2.08 27 1.233 BD 1.84 1.079 BE 0.9 29 1.12 B 1.29 30 0.959 BE 1.79 31 1.229 CA 1.46 32 1.027 CA 1.97 33 1.109 CA 2.29 34 1.118 CB 35 1.066 CB 2.06 36 1.146 CB 1.51 37 1.053 CC 1.47 38 1.082 CC 2.19 39 1.113 CC 2 40 1.14 CD 1.7 41 1.172 CD 2.87 0.966 CD 0.3 43 0.963 CE 2.18 44 1.064 CE 1.65 45 1.086 CE 2.59 46 0.985 DA 1.96 47 0.894 DA 2.43 48 1.109 DA 1.56 49 0.847 D B 1.51 50 0.799 DB 1.3 51 0.918 DB 0.7 52 1.033 DC 2.31 0.943 DC 1.85 54 1.089 DC 0.71 55 0.988 DD 1.12 1.169 D D 1.47 57 1.106 D D 2.9 58 1.308 DE 2.08 1.498 DE 1.94 60 1.271 DE 1.94 61 1.128 E A 1.03 1.141 E A 0.94 63 1.144 E A 0.15 64 0.99 E B 0.95 65 0.801 E B 1.69 66 0.416 EB 2.14 67 0.929 E C 1.3 68 0.95 EC 1.79 0.899 EC 1.11 70 0.873 E D 0.81 71 0.871 E D 1.65 72 0.786 ED 0.61 73 0.93 E E 1.88 74 0.968 E E 1.41 0.844 E E 1.22 In the calibration of HIV antibody tests, optical density of HIV antibodies was computed via Enzyme- Linked Immunosorbent Assay for a variety of lots and runs, and then compared to the more sensitive Western-blot test. (a) Perform a hypothesis test to assess whether or not optical density differs across lot or run or if they interact to an a = 0.01 level. Report the conclusions of your tests. (b) Assess the assumptions of your hypothesis test in a). (c) Perform a post-hoc test if appropriate and identify significant differences. If not appropriate, explain why. (d) Construct a model to predict Western blot concentration as a function of optical density from the ELISA. Write the equation that relates these two variables generated by your model estimate. (e) Perform an interpret a model utility test for your model in F. How much variability in Western blot concentration does optical density explain? (f) Assess the assumptions of your model constructed in d.
Sample opticalDens lot run westernBlot 1 1.053 A A 1.708 A A 2.99 0.977 A A 1.67 4 0.881 AB 1.47 0.788 A B 2.25 6 0.788 A B 0.15 7 0.896 AC 1.41 1.038 AC 2.51 9 0.963 AC 1.85 10 0.971 A D 1.7 11 1.234 AD 1.49 12 1.089 A D 1.92 13 0.984 A E 0.96 14 0.986 A E 1.64 15 1.067 A E 16 0.996 BA 1.77 17 1.129 BA 1.69 18 1.016 BA 3.01 19 1.019 B B 1.03 20 1.088 B B 1.94 21 1.28 BB 2.1 22 1.12 BC 0.83 23 1.054 BC 2.52 24 1.235 BC 1.78 1.327 BD 2.2 26 1.361 BD 2.08 27 1.233 BD 1.84 1.079 BE 0.9 29 1.12 B 1.29 30 0.959 BE 1.79 31 1.229 CA 1.46 32 1.027 CA 1.97 33 1.109 CA 2.29 34 1.118 CB 35 1.066 CB 2.06 36 1.146 CB 1.51 37 1.053 CC 1.47 38 1.082 CC 2.19 39 1.113 CC 2 40 1.14 CD 1.7 41 1.172 CD 2.87 0.966 CD 0.3 43 0.963 CE 2.18 44 1.064 CE 1.65 45 1.086 CE 2.59 46 0.985 DA 1.96 47 0.894 DA 2.43 48 1.109 DA 1.56 49 0.847 D B 1.51 50 0.799 DB 1.3 51 0.918 DB 0.7 52 1.033 DC 2.31 0.943 DC 1.85 54 1.089 DC 0.71 55 0.988 DD 1.12 1.169 D D 1.47 57 1.106 D D 2.9 58 1.308 DE 2.08 1.498 DE 1.94 60 1.271 DE 1.94 61 1.128 E A 1.03 1.141 E A 0.94 63 1.144 E A 0.15 64 0.99 E B 0.95 65 0.801 E B 1.69 66 0.416 EB 2.14 67 0.929 E C 1.3 68 0.95 EC 1.79 0.899 EC 1.11 70 0.873 E D 0.81 71 0.871 E D 1.65 72 0.786 ED 0.61 73 0.93 E E 1.88 74 0.968 E E 1.41 0.844 E E 1.22 In the calibration of HIV antibody tests, optical density of HIV antibodies was computed via Enzyme- Linked Immunosorbent Assay for a variety of lots and runs, and then compared to the more sensitive Western-blot test. (a) Perform a hypothesis test to assess whether or not optical density differs across lot or run or if they interact to an a = 0.01 level. Report the conclusions of your tests. (b) Assess the assumptions of your hypothesis test in a). (c) Perform a post-hoc test if appropriate and identify significant differences. If not appropriate, explain why. (d) Construct a model to predict Western blot concentration as a function of optical density from the ELISA. Write the equation that relates these two variables generated by your model estimate. (e) Perform an interpret a model utility test for your model in F. How much variability in Western blot concentration does optical density explain? (f) Assess the assumptions of your model constructed in d.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 33PPS
Question
Transcribed Image Text:Sample opticalDens lot run westernBlot
1
1.053 A A
1.708 A A
2.99
0.977 A A
1.67
4
0.881 AB
1.47
0.788 A B
2.25
6
0.788 A B
0.15
7
0.896 AC
1.41
1.038 AC
2.51
9
0.963 AC
1.85
10
0.971 A D
1.7
11
1.234 AD
1.49
12
1.089 A D
1.92
13
0.984 A E
0.96
14
0.986 A E
1.64
15
1.067 A E
16
0.996 BA
1.77
17
1.129 BA
1.69
18
1.016 BA
3.01
19
1.019 B B
1.03
20
1.088 B B
1.94
21
1.28 BB
2.1
22
1.12 BC
0.83
23
1.054 BC
2.52
24
1.235 BC
1.78
1.327 BD
2.2
26
1.361 BD
2.08
27
1.233 BD
1.84
1.079 BE
0.9
29
1.12 B
1.29
30
0.959 BE
1.79
31
1.229 CA
1.46
32
1.027 CA
1.97
33
1.109 CA
2.29
34
1.118 CB
35
1.066 CB
2.06
36
1.146 CB
1.51
37
1.053 CC
1.47
38
1.082 CC
2.19
39
1.113 CC
2
40
1.14 CD
1.7
41
1.172 CD
2.87
0.966 CD
0.3
43
0.963 CE
2.18
44
1.064 CE
1.65
45
1.086 CE
2.59
46
0.985 DA
1.96
47
0.894 DA
2.43
48
1.109 DA
1.56
49
0.847 D B
1.51
50
0.799 DB
1.3
51
0.918 DB
0.7
52
1.033 DC
2.31
0.943 DC
1.85
54
1.089 DC
0.71
55
0.988 DD
1.12
1.169 D D
1.47
57
1.106 D D
2.9
58
1.308 DE
2.08
1.498 DE
1.94
60
1.271 DE
1.94
61
1.128 E A
1.03
1.141 E A
0.94
63
1.144 E A
0.15
64
0.99 E B
0.95
65
0.801 E B
1.69
66
0.416 EB
2.14
67
0.929 E C
1.3
68
0.95 EC
1.79
0.899 EC
1.11
70
0.873 E D
0.81
71
0.871 E D
1.65
72
0.786 ED
0.61
73
0.93 E E
1.88
74
0.968 E E
1.41
0.844 E
E
1.22
Transcribed Image Text:In the calibration of HIV antibody tests, optical density of HIV antibodies was computed via Enzyme-
Linked Immunosorbent Assay for a variety of lots and runs, and then compared to the more sensitive
Western-blot test.
(a) Perform a hypothesis test to assess whether or not optical density differs across lot or run or if
they interact to an a = 0.01 level. Report the conclusions of your tests.
(b) Assess the assumptions of your hypothesis test in a).
(c) Perform a post-hoc test if appropriate and identify significant differences. If not appropriate,
explain why.
(d) Construct a model to predict Western blot concentration as a function of optical density from the
ELISA. Write the equation that relates these two variables generated by your model estimate.
(e) Perform an interpret a model utility test for your model in F. How much variability in Western
blot concentration does optical density explain?
(f) Assess the assumptions of your model constructed in d.
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