Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is $\mu _ { \mathrm { d } } = 0$. Compute the value of the $t$ test statistic.
-$$\begin{array} { c | c c c c c c c c }
\mathrm { x } & 7.1 & 5.9 & 3.4 & 10.3 & 4 & 10.2 & 9.3 & 7.1 \
\hline \mathrm { y } & 5.3 & 5.6 & 4.5 & 5.6 & 4.4 & 4.9 & 5.4 & 5.4
\end{array}$$
A)t = 6.792
B)t = 0.998
C)t = 2.391
D)t = 0.845

Question

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is $\mu _ { \mathrm { d } } = 0$. Compute the value of the $t$ test statistic.
-$$\begin{array} { c | c c c c c c c c } 
\mathrm { x } & 7.1 & 5.9 & 3.4 & 10.3 & 4 & 10.2 & 9.3 & 7.1 \
\hline \mathrm { y } & 5.3 & 5.6 & 4.5 & 5.6 & 4.4 & 4.9 & 5.4 & 5.4
\end{array}$$
A)t = 6.792
B)t = 0.998
C)t = 2.391
D)t = 0.845

Quizplus · Accepted Answer

To calculate the $t$ test statistic for paired sample data, we first find the differences between each pair of $x$ and $y$ values, then calculate the mean ($\bar{d}$) and standard deviation (s) of these differences. The formula for the $t$ test statistic is $t = \frac{\bar{d} - \mu_d}{s/\sqrt{n}}$, where $\mu_d = 0$ (the hypothesized mean difference), and $n$ is the number of pairs. Given the data, after calculating the differences, their mean, and standard deviation, applying the formula will give a $t$ value that matches the option C, which indicates it's the correct calculation for this dataset.

Assume That You Want to Test the Claim That the Paired