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.
$\begin{array} { l | l l l l l }
x & 9 & 6 & 7 & 5 & 12 \
\hline y & 6 & 8 & 3 & 6 & 7
\end{array}$
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.
$\begin{array} { l | l l l l l } 
x & 9 & 6 & 7 & 5 & 12 \
\hline y & 6 & 8 & 3 & 6 & 7
\end{array}$
A)  t=0.578 
B)  t=2.890 
C)  t=1.292 
D)  t=0.415

Quizplus · Accepted Answer

To calculate the t-test statistic for paired samples, we first find the differences between each pair of x and y, calculate the mean of these differences ($\bar{d}$), and the standard deviation of these differences (s_d). Then, we use the formula $t = \frac{\bar{d} - \mu_d}{s_d / \sqrt{n}}$, where $\mu_d = 0$ (hypothesized mean difference), and $n$ is the number of pairs.Differences (d) = x - y = [3, -2, 4, -1, 5]Mean of differences ($\bar{d}$) = (3 - 2 + 4 - 1 + 5) / 5 = 9 / 5 = 1.8Standard deviation of differences (s_d) can be calculated from the differences.Variance (s_d^2) = [((3-1.8)^2 + (-2-1.8)^2 + (4-1.8)^2 + (-1-1.8)^2 + (5-1.8)^2) / (5-1)] = [((1.2)^2 + (-3.8)^2 + (2.2)^2 + (-2.8)^2 + (3.2)^2) / 4] = (1.44 + 14.44 + 4.84 + 7.84 + 10.24) / 4 = 38.8 / 4 = 9.7Standard deviation (s_d) = sqrt(9.7) ≈ 3.1145Using the formula for the t-test statistic:$t = \frac{\bar{d} - \mu_d}{s_d / \sqrt{n}} = \frac{1.8 - 0}{3.1145 / \sqrt{5}} ≈ \frac{1.8}{3.1145 / 2.236} ≈ \frac{1.8}{1.3922} ≈ 1.292$Therefore, the correct answer is t=1.292.

Assume That You Want to Test the Claim That the Paired