Following is a sample of five matched pairs.
$\begin{array}{llllll}
\hline \text { Sample 1 } & 15 & 20 & 19 & 20 & 16 \
\text { Sample 2 } & 23 & 18 & 23 & 19 & 18 \
\hline
\end{array}$

Let $\mu _ { 1 }$ and $\mu _ { 2 }$ represent the population means and let $\mu _ { \mathrm { d } } = \mu _ { 1 } - \mu _ { 2 }$. A test will be made of the hypotheses $H _ { 0 } : \mu _ { \mathrm { d } } = 0$ versus $H _ { 1 } : \mu _ { \mathrm { d } } 0$. Compute the test statistic.
A) -1.222
B) -0.984
C) -0.547
D) -2.452

Question

Following is a sample of five matched pairs.
$\begin{array}{llllll}
\hline \text { Sample 1 } & 15 & 20 & 19 & 20 & 16 \
\text { Sample 2 } & 23 & 18 & 23 & 19 & 18 \
\hline
\end{array}$

Let $\mu _ { 1 }$ and $\mu _ { 2 }$ represent the population means and let $\mu _ { \mathrm { d } } = \mu _ { 1 } - \mu _ { 2 }$. A test will be made of the hypotheses $H _ { 0 } : \mu _ { \mathrm { d } } = 0$ versus $H _ { 1 } : \mu _ { \mathrm { d } } > 0$. Compute the test statistic.
A) -1.222
B) -0.984
C) -0.547
D) -2.452

Quizplus · Accepted Answer

The test statistic for matched pairs involves calculating the differences between each pair, finding the mean of these differences, and then dividing by the standard deviation of the differences divided by the square root of the number of pairs. The calculation leads to a test statistic of -1.222, indicating the correct choice is A.

Following Is a Sample of Five Matched Pairs Sample 1 1520192016 Sample 2 2318231918\begin{array}{llllll}\hline \text { Sample 1 } & 15 & 20 & 19 & 20 & 16 \\\text { Sample 2 } & 23 & 18 & 23 & 19 & 18 \\\hline\end{array} Sample 1 Sample 2 ​1523​2018​1923​2019​1618​​

Following Is a Sample of Five Matched Pairs $\begin{array}{llllll}\hline \text { Sample 1 } & 15 & 20 & 19 & 20 & 16 \\\text { Sample 2 } & 23 & 18 & 23 & 19 & 18 \\\hline\end{array}$