Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is $\mu _ { d } = 0$. Compute the value of the $t$ test statistics. Round intermediate calculations to four decimal places as needed and final answers to three decimal places as needed.
$\begin{array}{l|lllll}
x & 9 & 6 & 7 & 5 & 12 \
\hline y & 6 & 8 & 3 & 6 & 7
\end{array}$

A) $t = 0.578$
B) $t = 2.890$
C) $t = 1.292$
D) $t = 0.415$

Question

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is $\mu _ { d } = 0$. Compute the value of the $t$ test statistics. Round intermediate calculations to four decimal places as needed and final answers to three decimal places as needed.
$\begin{array}{l|lllll}
x & 9 & 6 & 7 & 5 & 12 \
\hline y & 6 & 8 & 3 & 6 & 7
\end{array}$

A) $t = 0.578$
B) $t = 2.890$
C) $t = 1.292$
D) $t = 0.415$

Quizplus · Accepted Answer

To compute the $t$ test statistic for paired data, first calculate the differences $d_i = x_i - y_i$, then find the mean $\bar{d}$ and standard deviation $s_d$ of these differences. The formula for the $t$ statistic is $t = \frac{\bar{d}}{s_d/\sqrt{n}}$, where $n$ is the number of pairs. After calculating, the $t$ value is approximately 1.292.

Assume That You Want to Test the Claim That the Paired