Thank you for visiting Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM Find the values of a tex bar. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
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
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