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9.3.2 Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM. Find the values of d overbar and s Subscript d. In​ general, what does mu Subscript d ​represent? Temperature (degrees Upper F )at 8 AM 98.1 98.8 97.3 97.5 97.9 Temperature (degrees Upper F )at 12 AM 98.7 99.4 97.7 97.1 98.0 Let the temperature at 8 AM be the first​ sample, and the temperature at 12 AM be the second sample. Find the values of d overbar and s Subscript d.

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Answer:


\frac{}{d} = −0.26


s_(d) = 0.4219

Explanation:

Given:

Sample1: 98.1 98.8 97.3 97.5 97.9

Sample2: 98.7 99.4 97.7 97.1 98.0

Sample 1 Sample 2 Difference d

98.1 98.7 -0.6

98.8 99.4 -0.6

97.3 97.7 -0.4

97.5 97.1 0.4

97.9 98.0 -0.1

To find:

Find the values of
\frac{}{d} and
s_(d)

d overbar (
\frac{}{d}) is the sample mean of the differences which is calculated by dividing the sum of all the values of difference d with the number of values i.e. n = 5


\frac{}{d} = ∑d/n

= (−0.6 −0.6 −0.4 +0.4 −0.1) / 5

= −1.3 / 5


\frac{}{d} = −0.26

s Subscript d is the sample standard deviation of the difference which is calculated as following:


s_(d) = √∑(
d_(i) -
\frac{}{d})²/ n-1


s_(d) =


(-0.6 - (-0.26))^(2) + (-0.6 - (-0.26))^(2) + (-0.4 - (-0.26))^(2) + (0.4-(-0.26))^(2) + (-0.1 - (-0.26))^(2) / 5-1

= √ (−0.6 − (−0.26 ))² + (−0.6 − (−0.26))² + (−0.4 − (−0.26))² + (0.4 −

(−0.26))² + (−0.1 − (−0.26))² / 5−1

=
\sqrt{(0.1156 + 0.1156 + 0.0196 + 0.4356 + 0.0256)/(4) }

=
\sqrt{(0.712)/(4) }

=
√(0.178)

= 0.4219


s_(d) = 0.4219

Subscript d ​represent

μ
_(d) represents the mean of differences in body temperatures measured at 8 AM and at 12 AM of population.

User Haymansfield
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