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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 \( \mu_d \) 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 :

Answer:

The value of [tex]\bar d[/tex] is -0.2.

The value of [tex]s_{\bar d}[/tex] is 0.3464.

[tex]\mu_{d}[/tex] = mean difference in body temperatures.

Step-by-step explanation:

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

The formula of [tex]\bar d[/tex] and [tex]s_{\bar d}[/tex] are:

[tex]\bar d=\frac{1}{n}\sum (x_{1}-x_{2})[/tex]

[tex]s_{\bar d}=\sqrt{\frac{1}{n-1}\sum (d_{i}-\bar d)^{2}}[/tex]

Consider the table below.

Compute the value of [tex]\bar d[/tex] as follows:

[tex]\bar d=\frac{1}{n}\sum (x_{1}-x_{2})=\frac{1}{5}\times-1=-0.2[/tex]

Thus, the value of [tex]\bar d[/tex] is -0.2.

Compute the value of [tex]s_{\bar d}[/tex] as follows:

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

Thus, the value of [tex]s_{\bar d}[/tex] is 0.3464.

The variable [tex]\mu_{d}[/tex] represents the mean difference in body temperatures measured at 8 AM and again at 12 AM.

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