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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: 97.5, 97.1, 97.7, 97.2, 98.7
Temperature (°F) at 12 AM: 98.1, 99.2, 97.5, 97.6, 97.5

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

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

In general, what does [tex]\bar{d}[/tex] represent?

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

Click to select your answer(s).

Answer :

The values of mean difference and standard deviation are approximately 0.725 and 0.963, respectively.

In general, He (Wg) represents the mean value of the differences for the paired sample data. Therefore, the correct answer is C.

To find the values of mean difference and standard deviation , we need to calculate the differences between the temperatures at 8 AM and 12 AM for each subject and then perform some calculations.

Given temperatures at 8 AM:

97.5, 97.1, 97.7, 97.2

And temperatures at 12 AM:

98.1, 99.2, 97.5, 97.6

We subtract the temperature at 8 AM from the temperature at 12 AM for each subject:

0.6, 2.1, -0.2, 0.4

To find mean difference, we calculate the mean of these differences:

d = (0.6 + 2.1 - 0.2 + 0.4) / 4 = 2.9 / 4 = 0.725

To find standard deviation , we calculate the sample standard deviation of these differences:

Step 1: Calculate the squared differences from the mean (0.725) for each difference:

(0.6 - 0.725)², (2.1 - 0.725)², (-0.2 - 0.725)², (0.4 - 0.725)²

Step 2: Calculate the sum of these squared differences:

(0.00625 + 1.208025 + 1.490625 + 0.081225) = 2.786125

Step 3: Divide the sum by (n - 1), where n is the number of differences (4 in this case):

2.786125 / (4 - 1) = 2.786125 / 3 ≈ 0.92871

Step 4: Take the square root of the result:

sg ≈ √0.92871 ≈ 0.963

Therefore, the values of mean difference and standard deviation are approximately 0.725 and 0.963, respectively.

Regarding the second part of the question, Wg represents:

C. The mean value of the differences for the paired sample data.

Learn more about standard deviation here:

https://brainly.com/question/13498201

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