Answer :
a) d-bar (mean of differences): 0.4
b) sub d (standard deviation of differences): approximately 0.363
c) The mean d represents the average change or difference between the values in two sets of observations. In this specific case, it represents the average change in body temperature from 8 AM to 12 AM across the five subjects.
To find the values of d-bar and sub d, we first need to calculate the differences between the temperatures at 8 AM and 12 AM for each subject.
Temperatures at 8 AM: 98.3, 98.9, 97.2, 97.1, 97.4
Temperatures at 12 AM: 98.7, 99.3, 97.7, 96.7, 97.9
Calculating the differences:
d1 = (temperature at 12 AM) - (temperature at 8 AM)
d2 = (temperature at 12 AM) - (temperature at 8 AM)
d3 = (temperature at 12 AM) - (temperature at 8 AM)
d4 = (temperature at 12 AM) - (temperature at 8 AM)
d5 = (temperature at 12 AM) - (temperature at 8 AM)
d1 = 98.7 - 98.3 = 0.4
d2 = 99.3 - 98.9 = 0.4
d3 = 97.7 - 97.2 = 0.5
d4 = 96.7 - 97.1 = -0.4
d5 = 97.9 - 97.4 = 0.5
a) d-bar (mean of differences):
d-bar = (d1 + d2 + d3 + d4 + d5) / 5
= (0.4 + 0.4 + 0.5 - 0.4 + 0.5) / 5
= 0.4
b) sub d (standard deviation of differences):
To calculate the standard deviation of differences, we first find the squared differences and then take the square root of their average.
Squared differences:
[tex](d1 - d-bar)^2, (d2 - d-bar)^2, (d3 - d-bar)^2, (d4 - d-bar)^2, (d5 - d-bar)^2\\(d1 - d-bar)^2 = (0.4 - 0.4)^2 = 0\\(d2 - d-bar)^2 = (0.4 - 0.4)^2 = 0\\(d3 - d-bar)^2 = (0.5 - 0.4)^2 = 0.01\\(d4 - d-bar)^2 = (-0.4 - 0.4)^2 = 0.64\\(d5 - d-bar)^2 = (0.5 - 0.4)^2 = 0.01[/tex]
Calculating the average of squared differences:
[tex](sub d)^2 = [(d1 - d-bar)^2 + (d2 - d-bar)^2 + (d3 - d-bar)^2 + (d4 - d-bar)^2 + (d5 - d-bar)^2] / 5[/tex]
= (0 + 0 + 0.01 + 0.64 + 0.01) / 5
= 0.132
[tex]sub d = sqrt((sub d)^2)[/tex]
= sqrt(0.132)
≈ 0.363
c) In general, the mean d represents the average difference between the values in two sets of observations. In this case, it represents the average change in body temperature from 8 AM to 12 AM across the five subjects.
Learn more about deviation: https://brainly.in/question/4593664
#SPJ11