Answer :
The [tex]\overline d[/tex] = 0.04 and [tex]s_d[/tex] ≈ 0.433. The [tex]mu_d[/tex] represents the mean of the differences from the population of matched data (Option c).
To find the values of overline d (mean of differences) and [tex]s_d[/tex] (standard deviation of differences), we need to calculate the differences between the temperature measurements at 8 AM and 12 AM for each subject.
Here are the temperature measurements at 8 AM:
97.9, 99.4, 97.4, 97.4, 97.3
And here are the temperature measurements at 12 AM:
98.5, 99.7, 97.6, 97.1, 97.5
Now, let's calculate the differences and find overline d and [tex]s_d[/tex]:
Differences (d):
98.5 - 97.9 = 0.6
99.7 - 99.4 = 0.3
97.6 - 97.4 = 0.2
97.1 - 97.4 = -0.3
97.5 - 97.3 = 0.2
Mean of Differences ([tex]\overline d[/tex]):
[tex]\overline d[/tex] = (0.6 + 0.3 + 0.2 - 0.3 + 0.2) / 5 = 0.2 / 5 = 0.04
Standard Deviation of Differences ([tex]s_d[/tex]):
First, calculate the squared differences:
(0.6 - 0.04)² = 0.3136
(0.3 - 0.04)² = 0.2025
(0.2 - 0.04)² = 0.0256
(-0.3 - 0.04)² = 0.3721
(0.2 - 0.04)² = 0.0256
Then, calculate the variance:
Variance ([tex]s_d^2[/tex]) = (0.3136 + 0.2025 + 0.0256 + 0.3721 + 0.0256) / 5 = 0.18768
Finally, take the square root of the variance to get the standard deviation:
[tex]s_d[/tex] = √(0.18768) ≈ 0.433
Therefore, [tex]\overline d[/tex] = 0.04 and [tex]s_d[/tex] ≈ 0.433.
Now, let's determine what [tex]mu_d[/tex] represents:
[tex]mu_d[/tex] represents:
C. The mean of the differences from the population of matched data
The complete question is:
Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM. Find the values of overline d and [tex]s_{d}[/tex] In general, what does [tex]H_d[/tex] represent?
Temperature overline at 8 AM 97.9 99.4 97.4 97.4 97.3
Temperature at 12 AM 98.5 99.7 97.6 97.1 97.5
[tex]\overline 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_{d}[/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
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