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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

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

MATLAB: An Introduction with Applications
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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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 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 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
Transcribed Image Text:" 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
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