Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 PM. Find the values of [tex]d[/tex] and [tex]s_d[/tex]. In general, what does [tex]\mu[/tex] represent?

Temperature (°F) at 8 AM:
- 97.6
- 99.4
- 97.6
- 97.7
- 97.4

Temperature (°F) at 12 PM:
- 98.0
- 99.9
- 97.9
- 97.4
- 97.6

Let the temperature at 8 AM be the first sample, and the temperature at 12 PM be the second sample.

Find the values of [tex]d[/tex] and [tex]s_d[/tex].
- [tex]d = [/tex] (Type an integer or a decimal. Do not round.)
- [tex]s_d = [/tex] (Round to two decimal places as needed.)

In general, what does [tex]\mu[/tex] represent?
A. The mean value of the differences for the paired sample data.
B. The mean of the means of each matched pair from the population of matched data.
C. The mean of the differences from the population of matched data.
D. The difference of the population means of the two populations.

To calculate the values of d and s for the paired sample data, we need to first find the differences between the temperature at 8 AM and 12 AM for each subject.

The differences are:

99.9 - 97.6 = 2.3

97.9 - 99.4 = -1.5

97.4 - 97.6 = -0.2

97.6 - 97.7 = -0.1

The mean value of these differences (d) is:

d = (2.3 - 1.5 - 0.2 - 0.1) / 4 = 0.125

The standard deviation of these differences (sd) is:

sd = sqrt([(-2.175)^2 + (0.375)^2 + (0.025)^2 + (0.025)^2] / 3) = 1.12 (rounded to two decimal places)

In general, d represents the mean value of the differences for the paired sample data. It measures the average amount by which the second measurement differs from the first measurement. The sign of d indicates the direction of change - a positive value means an increase in the second measurement, and a negative value means a decrease. The sd represents the variability or dispersion of the differences around the mean value.

Learn more about deviation here:

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