To find the standard deviation of the paired differences ($d$), we first calculate the differences between the body temperatures before and after taking the drug. Then, we calculate the standard deviation of these differences.

Step 1: Calculate the differences ($d$)

For each subject: $d = \text{Temperature (after)} - \text{Temperature (before)}$

$d_1 = 98.8 - 99.1 = -0.3$ $d_2 = 99.3 - 99.9 = -0.6$ $d_3 = 99.6 - 98.9 = 0.7$ $d_4 = 98.5 - 98.8 = -0.3$ $d_5 = 99.5 - 99.7 = -0.2$ $d_6 = 99.3 - 99.8 = -0.5$ $d_7 = 99.4 - 99.9 = -0.5$

The differences ($d$) are: $d = [-0.3, -0.6, 0.7, -0.3, -0.2, -0.5, -0.5]$

Step 2: Calculate the mean of $d$

The mean of $d$ ($\bar{d}$) is: $\bar{d} = \frac{\sum d}{n} = \frac{-0.3 + (-0.6) + 0.7 + (-0.3) + (-0.2) + (-0.5) + (-0.5)}{7}$ $\bar{d} = \frac{-1.7}{7} = -0.242857 \approx -0.24$

Step 3: Calculate the deviations from the mean

For each $d_i$, calculate $(d_i - \bar{d})^2$: $(d_1 - \bar{d})^2 = (-0.3 - (-0.24))^2 = (-0.06)^2 = 0.0036$ $(d_2 - \bar{d})^2 = (-0.6 - (-0.24))^2 = (-0.36)^2 = 0.1296$ $(d_3 - \bar{d})^2 = (0.7 - (-0.24))^2 = (0.94)^2 = 0.8836$ $(d_4 - \bar{d})^2 = (-0.3 - (-0.24))^2 = (-0.06)^2 = 0.0036$ $(d_5 - \bar{d})^2 = (-0.2 - (-0.24))^2 = (0.04)^2 = 0.0016$ $(d_6 - \bar{d})^2 = (-0.5 - (-0.24))^2 = (-0.26)^2 = 0.0676$ $(d_7 - \bar{d})^2 = (-0.5 - (-0.24))^2 = (-0.26)^2 = 0.0676$

Step 4: Calculate the variance

The variance ($s^2$) of the differences is: $s^2 = \frac{\sum (d_i - \bar{d})^2}{n-1}$ $s^2 = \frac{0.0036 + 0.1296 + 0.8836 + 0.0036 + 0.0016 + 0.0676 + 0.0676}{7-1}$ $s^2 = \frac{1.1572}{6} \approx 0.1929$

Step 5: Calculate the standard deviation

The standard deviation ($s$) is the square root of the variance: $s = \sqrt{0.1929} \approx 0.44$

Final Answer:

The standard deviation of the paired differences is: $\boxed{0.44}$

Let me know if you'd like to proceed with additional steps in the hypothesis test or need further clarification!

Relative Questions:

1. What is the next step in conducting the hypothesis test for paired differences?
2. How do we determine the test statistic for this problem?
3. What role does the significance level ($\alpha$) play in this test?
4. How do we interpret a result when $p$-value < $\alpha$?
5. What assumptions must hold for a paired $t$-test to be valid?

Tip: Always verify normality assumptions in paired $t$-tests, especially for small sample sizes.