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Answer :
The average difference (d(bar)) between the temperatures at 8AM and 12AM is 0.675, and the standard deviation (sd) is approximately 0.189.
To find the values of d and sd, we need to calculate the differences between the temperatures at 8AM and 12AM for each subject and then analyze those differences.
Given the following body temperature data:
Temperature (oF) at 8 AM: 97.7, 98.5, 97.6, 97.5
Temperature (oF) at 12 AM: 98.5, 99.3, 98.3, 97.9
Step 1: Calculate the differences (d) between the temperatures at 8AM and 12AM for each subject.
d = (Temperature at 12 AM) - (Temperature at 8 AM)
For the given data, the differences (d) are as follows:
d1 = 98.5 - 97.7 = 0.8
d2 = 99.3 - 98.5 = 0.8
d3 = 98.3 - 97.6 = 0.7
d4 = 97.9 - 97.5 = 0.4
Step 2: Calculate the average of the differences (dˉ).
dˉ = (d1 + d2 + d3 + d4) / 4 = (0.8 + 0.8 + 0.7 + 0.4) / 4 = 2.7 / 4 = 0.675
Therefore, the average difference (dˉ) is 0.675.
Step 3: Calculate the standard deviation of the differences (sd).
To calculate sd, we need to find the deviations from the average difference (dˉ), square each deviation, calculate the sum of squared deviations, divide it by (n-1), and finally take the square root.
Squared deviations:
(d1 - dˉ)^2 = (0.8 - 0.675)^2 = 0.015625
(d2 - dˉ)^2 = (0.8 - 0.675)^2 = 0.015625
(d3 - dˉ)^2 = (0.7 - 0.675)^2 = 0.000625
(d4 - dˉ)^2 = (0.4 - 0.675)^2 = 0.075625
Sum of squared deviations:
0.015625 + 0.015625 + 0.000625 + 0.075625 = 0.1075
Divide the sum by (n-1):
0.1075 / 3 = 0.03583333333
Take the square root:
sd = √(0.03583333333) ≈ 0.189395333
Therefore, the standard deviation of the differences (sd) is approximately 0.189.
In general, μd represents the mean difference between paired observations. It provides information about the average change or effect observed when comparing two related measurements or conditions.
To learn more about standard deviation (sd) click here: brainly.com/question/34173072
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