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

Temperature (°F) at 8 AM: 97.9, 99.4, 97.4, 97.4, 97.3
Temperature (°F) at 12 AM: 98.5, 99.7, 97.6, 97.1, 97.5

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

1. Find the values of [tex]d[/tex] and [tex]S_d[/tex]. (Type an integer or a decimal. Do not round.)
2. In general, what does [tex]H_a[/tex] represent?

A. The difference of the population means of the two populations
B. The mean value of the differences for the paired sample data
C. The mean of the differences from the population of matched data
D. The mean of the means of each matched pair from the population of matched data

Answer :

Given Data: Temperature (°F) at 8 AM 97.9, 99.4, 97.4, 97.4, 97.3 Temperature (°F) at 12 AM 98.5 99.7, 97.6, 97.1, 97.5 We need to find the values of d and Sd where d is the difference between the two sample means and Sd is the standard deviation of the differences.

The correct answer option is B.

d = μ1 - μ2 Here,μ1 is the mean of the temperature at 8 AM.μ2 is the mean of the temperature at 12 AM.

So, μ1 = (97.9 + 99.4 + 97.4 + 97.4 + 97.3)/5

= 97.88 And,

μ2 = (98.5 + 99.7 + 97.6 + 97.1 + 97.5)/5

= 98.28 Now,

d = μ1 - μ2

= 97.88 - 98.28

= -0.4 To find Sd, we need to use the formula

Sd = √[(Σd²)/n - (Σd)²/n²]/(n - 1) where n is the number of pairs. So, the differences are

0.6, -0.3, -0.2, 0.3, -0.2d² = 0.36, 0.09, 0.04, 0.09, 0.04Σd

= 0Σd² = 0.62 + 0.09 + 0.04 + 0.09 + 0.04

= 0.62Sd

= √[(Σd²)/n - (Σd)²/n²]/(n - 1)

= √[0.62/5 - 0/25]/4

= 0.13 Therefore, the value of d is -0.4 and Sd is 0.13. The mean value of the differences for the paired sample data represents what Hd represents in general.

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