Test Hypotheses Regarding Matched-Pairs Data
-Data sets $\mathrm { A }$ and $\mathrm { B }$ are dependent. Find $\mathrm { s } _ { \mathrm { d } }$.
$\begin{array}{c|ccccc}
\mathrm{A} & 6.4 & 7.4 & 9.3 & 6.3 & 6.4 \
\hline \mathrm{B} & 8.8 & 7.7 & 7.6 & 7.5 & 8.9
\end{array}$

Assume that the paired data came from a population that is normally distributed.
A) $1.73$
B) $1.21$
C) $1.32$
D) $1.89$

Question

Test Hypotheses Regarding Matched-Pairs Data
-Data sets $\mathrm { A }$ and $\mathrm { B }$ are dependent. Find $\mathrm { s } _ { \mathrm { d } }$.
$\begin{array}{c|ccccc}
\mathrm{A} & 6.4 & 7.4 & 9.3 & 6.3 & 6.4 \
\hline \mathrm{B} & 8.8 & 7.7 & 7.6 & 7.5 & 8.9
\end{array}$

Assume that the paired data came from a population that is normally distributed.
A) $1.73$
B) $1.21$
C) $1.32$
D) $1.89$

Quizplus · Accepted Answer

To find the standard deviation of the differences ($s_d$), first calculate the differences between each pair of A and B, then find the mean of these differences ($\bar{d}$), and finally calculate the standard deviation of these differences. The differences (B - A) are $2.4, 0.3, -1.7, 1.2, 2.5$. The mean of these differences is $\bar{d} = 0.94$. The squared differences from the mean are $2.19, 0.41, 6.89, 0.07, 2.43$. The sum of these squared differences is $12.09$. Divide by $n-1$ (where $n = 5$), we get $12.09 / 4 = 3.0225$. The square root of $3.0225$ is approximately $1.73$, which is the standard deviation of the differences.

Test Hypotheses Regarding Matched-Pairs Data -Data Sets A\mathrm { A }A

Test Hypotheses Regarding Matched-Pairs Data
-Data Sets $\mathrm { A }$