Answer :
d = 0.32, sd ≈ 0.36, and in general, μ2 represents the mean of the differences from the population of matched data (Option B). Thevalue of d, which represents the differences between paired samples, can be calculated by subtracting the temperature at 8 AM from the temperature at 12 AM.
The value of sd, the standard deviation of the differences, can be calculated to measure the variability of the paired sample differences.
To calculate the value of d, we subtract the temperature at 8 AM from the temperature at 12 AM for each pair of measurements. The differences are as follows:
d = 99.2 - 98.5, 99.8 - 99.2, 97.7 - 97.4, 97.8 - 97.9, 97.5 - 97.4
Calculating these differences, we get d = 0.7, 0.6, 0.3, -0.1, 0.1.
To find the value of sd, the standard deviation of the differences, we calculate the sample standard deviation of these differences. First, we find the mean of the differences: (0.7 + 0.6 + 0.3 - 0.1 + 0.1) / 5 = 0.32. Then, we calculate the sum of squared differences from the mean: (0.7 - 0.32)^2 + (0.6 - 0.32)^2 + (0.3 - 0.32)^2 + (-0.1 - 0.32)^2 + (0.1 - 0.32)^2 = 0.5084. Dividing this sum by n-1 (n = 5) and taking the square root gives us the sample standard deviation, sd ≈ 0.36.
In general, μ2 represents option B: The mean of the differences from the population of matched data. It refers to the average value of the paired sample differences in the population of interest.
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