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.

= −0.26

= 0.4219

Step-by-step 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 and

d overbar ( )  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

= ∑d/n

 = (−0.6 −0.6 −0.4 +0.4 −0.1) / 5

 = −1.3 / 5

= −0.26

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

= √∑( - )²/ n-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

=  

=

=

= 0.4219

= 0.4219

Subscript d represent

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