Following is a sample of five matched pairs.
$\begin{array}{llllll}
\hline \text { Sample 1 } & 23 & 26 & 18 & 32 & 28 \
\text { Sample 2 } & 19 & 14 & 16 & 12 & 14 \
\hline
\end{array}$

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) 4.651
B) 1.405
C) 8.547
D) 3.141

Question

Following is a sample of five matched pairs.
$\begin{array}{llllll}
\hline \text { Sample 1 } & 23 & 26 & 18 & 32 & 28 \
\text { Sample 2 } & 19 & 14 & 16 & 12 & 14 \
\hline
\end{array}$

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) 4.651
B) 1.405
C) 8.547
D) 3.141

Quizplus · Accepted Answer

The test statistic is calculated using the differences between the paired samples. The differences are 4, 12, 2, 20, and 14. The mean difference is 10.4, and the standard deviation of the differences is 7.77. The test statistic is calculated as $ t = \frac{\bar{d} - 0}{s_d/\sqrt{n}} $, which results in approximately 3.141.

Following Is a Sample of Five Matched Pairs Sample 1 2326183228 Sample 2 1914161214\begin{array}{llllll}\hline \text { Sample 1 } & 23 & 26 & 18 & 32 & 28 \\\text { Sample 2 } & 19 & 14 & 16 & 12 & 14 \\\hline\end{array} Sample 1 Sample 2 ​2319​2614​1816​3212​2814​​

Following Is a Sample of Five Matched Pairs $\begin{array}{llllll}\hline \text { Sample 1 } & 23 & 26 & 18 & 32 & 28 \\\text { Sample 2 } & 19 & 14 & 16 & 12 & 14 \\\hline\end{array}$