Assume that the differences are normally distributed. Complete parts (a) through (d) below.
$Unknown environment 'tabular'$
(a) Determine $d_{i} = X_{i} - Y_{i}$ for each pair of data.
$Unknown environment 'tabular'$
(Type integers or decimals.)
(b) Compute $\bar{d}$ and $s_{d}$
$\overset{―}{d} = ◻$ (Round to three decimal places as needed.)

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Take the square root of the variance to get the standard deviation, $s_{d} = \sqrt{s_{d}^{2}}$

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Step 1 ：Calculate the difference between each pair of data, $d_{i} = X_{i} - Y_{i}$ , to get: $- 3.5, 0.1, - 4.9, - 5.6, - 1.8, - 3.2, - 4.6, - 2.7$

Step 2 ：Compute the mean of these differences, $\bar{d} = \frac{- 3.5 + 0.1 - 4.9 - 5.6 - 1.8 - 3.2 - 4.6 - 2.7}{8} = - 3.275$

Step 3 ：Compute the variance of these differences, $s_{d}^{2} = \frac{(- 3.5 - (- 3.275))^{2} + (0.1 - (- 3.275))^{2} + (- 4.9 - (- 3.275))^{2} + (- 5.6 - (- 3.275))^{2} + (- 1.8 - (- 3.275))^{2} + (- 3.2 - (- 3.275))^{2} + (- 4.6 - (- 3.275))^{2} + (- 2.7 - (- 3.275))^{2}}{8 - 1}$

Step 4 ：Take the square root of the variance to get the standard deviation, $s_{d} = \sqrt{s_{d}^{2}}$

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