Assume that you want to test the claim that the paired sample data come from a population for which the mean difference
is $\mu _ { \mathrm { d } } = 0$ 0. Compute the value of the t test statistic. Round intermediate calculations to four decimal places as needed and
final answers to three decimal places as needed.
-$\begin{array}{c|cccccccc}
\mathrm{x} & 8.1 & 5.2 & 5.4 & 8.9 & 4.4 & 12.1 & 8.9 & 6.2 \
\hline \mathrm{y} & 6.3 & 4.9 & 6.5 & 4.2 & 4.8 & 6.8 & 5 & 4.5
\end{array}$

A) $t = 2.391$
B) $t = 0.998$
C) $t = 0.845$
D) $t = 6.792$

Question

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference
is $\mu _ { \mathrm { d } } = 0$ 0. Compute the value of the t test statistic. Round intermediate calculations to four decimal places as needed and
final answers to three decimal places as needed.
-$\begin{array}{c|cccccccc}
\mathrm{x} & 8.1 & 5.2 & 5.4 & 8.9 & 4.4 & 12.1 & 8.9 & 6.2 \
\hline \mathrm{y} & 6.3 & 4.9 & 6.5 & 4.2 & 4.8 & 6.8 & 5 & 4.5
\end{array}$

A) $t = 2.391$
B) $t = 0.998$
C) $t = 0.845$
D) $t = 6.792$

Quizplus · Accepted Answer

First, we need to calculate the difference between x and y for each pair. We get the following differences:

$$ 8.1-6.3=1.8, 5.2-4.9=0.3, 5.4-6.5=-1.1, 8.9-4.2=4.7, 4.4-4.8=-0.4, 12.1-6.8=5.3, 8.9-5=3.9, 6.2-4.5=1.7$$

Next, we calculate the mean difference and the standard deviation of the differences:

$$ \bar{d} = \frac{1.8 + 0.3 - 1.1 + 4.7 - 0.4 + 5.3 + 3.9 + 1.7}{8} = 2.025$$

$$s_d = \sqrt{\frac{\sum_{i=1}^8 (d_i - \bar{d})^2}{n-1}} = \sqrt{\frac{35.31}{7}} = 1.985$$

Finally, we calculate the t-test statistic:

$$t = \frac{\bar{d} - \mu_{d}}{\frac{s_d}{\sqrt{n}}} = \frac{2.025 - 0}{\frac{1.985}{\sqrt{8}}} = 2.391$$

We round the t-statistic to three decimal places to get the final answer of 2.391. Thus, the best choice is A.

Assume That You Want to Test the Claim That the Paired