the brain, which can be viewed using PET imaging. The radiotracer has a reported half-life of 14 hours, where its radioactivity will be below detection threshold. A random sample of 40 solutions of the dye is made up at the same concentration and their specific activities measured by a scintillation counter. The average half-life of these dyes is 14.3 hours. Assume that half-life is normally distributed with a standard deviation of 0.58 hours. Is there evidence to support the claim that the mean half-life exceeds 14 hours? Use a 5% level of significance. Your answer should include: State the statistical hypotheses (using
Medical researchers have developed a radiotracer dye that can bind to specific dopaminergic cell receptor sites in the brain, which can be viewed using PET imaging. The radiotracer has a reported half-life of 14 hours, where its radioactivity will be below detection threshold. A random sample of 40 solutions of the dye is made up at the same concentration and their specific activities measured by a scintillation counter. The average half-life of these dyes is 14.3 hours. Assume that half-life is
Your answer should include:
State the statistical hypotheses (using the appropriate notation).
Indicate whether the alternative hypothesis is non-directional or directional (and how you know).
Set the decision rules, which will include:
o State alpha
o Providing the critical value for the test statistic
o Sketch the curve and label the rejection region
o State the decision rules using the critical value approach
Calculate the test statistic
Draw a conclusion (state whether H0 is rejected or not and why you made this decision).
Interpret the result.
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How did you find the critical Value in regards to my z Table? If you could help me with figuring this out, I would appreciate it as I want to practice this as much as possible and learn how to do it well! Included is my Z table and T table from my textbook that goes with question - forgot to include.
Thank you in advance
!["
TABLE B-1 The z Distribution
Normal curve columns represent percentages between the mean and the z scores and percentages
beyond the z scores in the tail.
Z
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.12
Mean z
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.20
0.21
0.22
0.23
0.24
0.50
0.51
0.52
0.53
0.54
0.55
0.56
0.57
0.58
0.59
0.60
0.61
0.62
0.63
0.64
0.65
0.66
0.67
0.68
0.69
0.70
0.71
0.72
0.73
0.74
0.75
0.76
0.77
0.78
0.79
0.80
0.81
Mean z
% Mean to z
0.00
0.40
0.80
1.20
1.60
1.99
2.39
2.79
3.19
3.59
3.98
4.38
4.78
5.17
5.57
5.96
6.36
6.75
7.14
7.53
7.93
8.32
8.71
9.10
9.48
19.15
19.50
19.85
20.19
20.54
20.88
21.23
21.57
21.90
22.24
22.57
22.91
23.24
23.57
23.89
24.22
24.54
24.86
25.17
25.49
25.80
26.11
26.42
26.73
27.04
27.34
27.64
27.94
28.23
28.52
28.81
29.10
lil
% in Tail
50.00
49.60
49.20
48.80
48.40
48.01
47.61
47.21
46.81
46.41
46.02
45.62
45.22
44.83
44.43
44.04
43.64
43.25
42.86
42.47
42.07
41.68
41.29
40.90
40.52
30.85
30.50
30.15
29.81
29.46
29.12
28.77
28.43
28.10
27.76
27.43
27.09
26.76
26.43
26.11
25.78
25.46
25.14
24.83
24.51
24.20
23.89
23.58
23.27
22.96
22.66
22.36
22.06
21.77
21.48
21.19
20.90
Л
Z
0.25
0.26
0.27
0.28
0.29
0.30
0.31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
0.39
0.40
0.41
0.42
0.43
0.44
0.45
0.46
0.47
0.48
0.49
Mean z
0.87
0.88
0.89
0.90
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1.00
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
1.09
1.10
1.11
1.12
1.13
1.14
1.15
1.16
1.17
1.18
s
Mean z
% Mean to z
9.87
10.26
10.64
11.03
11.41
11.79
12.17
12.55
12.93
13.31
13.68
14.06
14.43
14.80
15.17
15.54
15.91
16.28
16.64
17.00
17.36
17.72
18.08
18.44
18.79
30.78
31.06
31.33
31.59
31.86
32.12
32.38
32.64
32.89
33.15
33.40
33.65
33.89
34.13
34.38
34.61
34.85
35.08
35.31
35.54
35.77
35.99
36.21
36.43
36.65
36.86
37.08
37.29
37.49
37.70
37.90
38.10
% in Tail
40.13
39.74
39.36
38.97
38.59
38.21
37.83
37.45
37.07
36.69
36.32
35.94
35.57
35.20
34.83
34.46
34.09
33.72
33.36
33.00
32.64
32.28
31.92
31.56
31.21
19.22
18.94
18.67
18.41
18.14
17.88
17.62
17.36
17.11
16.85
16.60
16.35
16.11
15.87
15.62
15.39
15.15
14.92
14.69
14.46
14.23
14.01
13.79
13.57
13.35
13.14
12.92
12.71
12.51
12.30
12.10
11.90
0.81
0.82
0.83
0.84
0.85
0.86
1.24
1.25
1.26
1.27
1.28
1.29
1.30
1.31
1.32
1.33
1.34
1.35
1.36
1.37
1.38
1.39
1.40
1.41
1.42
1.43
1.44
1.45
1.46
1.47
1.48
1.49
1.50
1.51
1.52
1.53
1.54
1.55
1.56
1.57
1.58
1.59
1.60
1.61
2.00
2.01
2.02
2.03
2.04
2.05
2.06
2.07
2.08
2.09
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
29.10
29.39
29.67
29.95
30.23
30.51
39.25
39.44
39.62
39.80
39.97
40.15
40.32
40.49
40.66
40.82
40.99
41.15
41.31
41.47
41.62
41.77
41.92
42.07
42.22
42.36
42.51
42.65
42.79
42.92
43.06
43.19
43.32
43.45
43.57
43.70
43.82
43.94
44.06
44.18
44.29
44.41
44.52
44.63
47.72
47.78
47.83
47.88
47.93
47.98
48.03
48.08
48.12
48.17
48.21
48.26
48.30
48.34
48.38
48.42
48.46
48.50
48.54
20.90
20.61
20.33
20.05
19.77
19.49
10.75
10.56
10.38
10.20
10.03
9.85
9.68
9.51
9.34
9.18
9.01
8.85
8.69
8.53
8.38
8.23
8.08
7.93
7.78
7.64
7.49
7.35
7.21
7.08
6.94
6.81
6.68
6.55
6.43
6.30
6.18
6.06
5.94
5.82
5.71
5.59
5.48
5.37
2.28
2.22
2.17
2.12
2.07
2.02
1.97
1.92
1.88
1.83
1.79
1.74
1.70
1.66
1.62
1.58
1.54
1.50
1.46
1.18
1.19
1.20
1.21
1.22
1.23
1.62
1.63
1.64
1.65
1.66
1.67
1.68
1.69
1.70
1.71
1.72
1.73
1.74
1.75
1.76
1.77
1.78
1.79
1.80
1.81
1.82
1.83
1.84
1.85
1.86
1.87
1.88
1.89
1.90
1.91
1.92
1.93
1.94
1.95
1.96
1.97
1.98
1.99
2.37
2.38
2.39
2.40
2.41
2.42
2.43
2.44
2.45
2.46
2.47
2.48
2.49
2.50
2.51
2.52
2.53
2.54
2.55
38.10
38.30
38.49
38.69
38.88
39.07
44.74
44.84
44.95
45.05
45.15
45.25
45.35
45.45
45.54
45.64
45.73
45.82
45.91
45.99
46.08
46.16
46.25
46.33
46.41
46.49
46.56
46.64
46.71
46.78
46.86
46.93
46.99
47.06
47.13
47.19
47.26
47.32
47.38
47.44
47.50
47.56
47.61
47.67
49.11
49.13
49.16
49.18
49.20
49.22
49.25
49.27
49.29
49.31
49.32
49.34
49.36
49.38
49.40
49.41
49.43
49.45
49.46
11.90
11.70
11.51
11.31
11.12
10.93
5.26
5.16
5.05
4.95
4.85
4.75
4.65
4.55
4.46
4.36
4.27
4.18
4.09
4.01
3.92
3.84
3.75
3.67
3.59
3.51
3.44
3.36
3.29
3.22
3.14
3.07
3.01
2.94
2.87
2.81
2.74
2.68
2.62
2.56
2.50
2.44
2.39
2.33
0.89
0.87
0.84
0.82
0.80
0.78
0.75
0.73
0.71
0.69
0.68
0.66
0.64
0.62
0.60
0.59
0.57
0.55
0.54](https://content.bartleby.com/qna-images/question/86c777ea-4c2e-45fd-992d-15b74d7a6644/1cfcb12d-aaa7-417c-b563-38a3b616d6d0/mxnoxan_thumbnail.png)
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