Question

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.

Answer 1

`\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.