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Answer :
The value of d represents the differences between the temperatures at 8 AM and 12 AM for each subject, and Sd represents the standard deviation of these differences.
To find the values of d and Sd (standard deviation), we need to calculate the differences between the corresponding temperatures at 8 AM and 12 AM for each subject. Let's denote the temperature at 8 AM as the first sample (x) and the temperature at 12 AM as the second sample (y).
Subject 1: d = x - y = 98.6 - 97.8 = 0.8
Subject 2: d = x - y = 97.7 - 98.2 = -0.5
Subject 3: d = x - y = 97.5 - 97.1 = 0.4
Subject 4: d = x - y = 97.8 - 96.8 = 1.0
Subject 5: d = x - y = 98.0 - 99.3 = -1.3
Next, we calculate the mean (average) of the differences:
Mean (μd) = (0.8 - 0.5 + 0.4 + 1.0 - 1.3) / 5 = 0.08
Then, we calculate the deviations of each difference from the mean:
d - μd:
0.8 - 0.08 = 0.72
-0.5 - 0.08 = -0.58
0.4 - 0.08 = 0.32
1.0 - 0.08 = 0.92
-1.3 - 0.08 = -1.38
We square each deviation:
(0.72)^2 = 0.5184
(-0.58)^2 = 0.3364
(0.32)^2 = 0.1024
(0.92)^2 = 0.8464
(-1.38)^2 = 1.9044
Next, we calculate the sum of squared deviations:
Σ(d - μd)^2 = 0.5184 + 0.3364 + 0.1024 + 0.8464 + 1.9044 = 3.708
Finally, we calculate the standard deviation (Sd) as the square root of the sum of squared deviations divided by (n - 1), where n is the number of samples:
Sd = sqrt(Σ(d - μd)^2 / (n - 1)) = sqrt(3.708 / (5 - 1)) = sqrt(3.708 / 4) = sqrt(0.927) ≈ 0.962
Therefore, the value of d represents the differences between the temperatures at 8 AM and 12 AM for each subject, and Sd represents the standard deviation of these differences.
Learn more about deviation here:
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