Question

Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM.

Find the values of d and s_d. In​ general, what does μ_d represent?
Temperature (°F)at 8 AM 97.5 99.3 97.8 97.5 97.4
Temperature (°F)at 12 AM 98.0 99.6 98.1 97.1 97.7

Answer 1

The value of
`\bar d` is -0.2.

The value of
`s_(\bar d)` is 0.3464.

`\mu_(d)` = mean difference in body temperatures.

Explanation:

The data for body temperatures from five different subjects measured at 8 AM and again at 12 AM are provided.

The formula of
`\bar d` and
`s_(\bar d)` are:

`\bar d=(1)/(n)\sum (x_(1)-x_(2))`

`s_(\bar d)=\sqrt{(1)/(n-1)\sum (d_(i)-\bar d)^(2)}`

Consider the table below.

Compute the value of
`\bar d` as follows:

`\bar d=(1)/(n)\sum (x_(1)-x_(2))=(1)/(5)*-1=-0.2`

Thus, the value of
`\bar d` is -0.2.

Compute the value of
`s_(\bar d)` as follows:

`s_(\bar d)=\sqrt{(1)/(n-1)\sum (d_(i)-\bar d)^(2)}=\sqrt{(0.48)/(4)}=0.3464`

Thus, the value of
`s_(\bar d)` is 0.3464.

The variable
`\mu_(d)` represents the mean difference in body temperatures measured at 8 AM and again at 12 AM.