Chapter 10, Problem 18CAP

1.

To determine

Find the value of the test statistic for a related-samples t test.

Answer to Problem 18CAP

The value of the test statistic for a related-samples t test is 2.

Explanation of Solution

Calculation:

The given information is that, $n_D=16,M_D=4,s_D=8$ and consider ${\mu }_D=0$.

Test statistic of related sample t test:

The formula for the test statistic of related sample t test is,

$\begin{array}{c}{t}_{\text{obt}}=\frac{M_D-{\mu }_D}{S_{MD}}\\ =\frac{M_D-{\mu }_D}{\frac{s_D}{\sqrt{n_D}}}\end{array}$

In formula, $M_D$ denotes the sample mean difference score, ${\mu }_D$ denotes the population mean difference and $S_{MD}=\frac{s_D}{\sqrt{n_D}}$ is the standard error for difference scores, $s_D$ is the standard deviation for difference score and $n_D$ is the sample size for difference scores.

Substitute values of, $n_D=16,M_D=4,s_D=8$ and ${\mu }_D=0$ in test statistic formula.

$\begin{array}{c}{t}_{\text{obt}}=\frac{4-0}{\left(\frac{8}{\sqrt{16}}\right)}\\ =\frac{4}{\left(\frac{8}{4}\right)}\\ =\frac{4}{2}\\ =2\end{array}$

Hence, the value of the test statistic for a related-samples t test is 2.

2.

To determine

Find the value of the test statistic for a related-samples t test.

Answer to Problem 18CAP

The value of the test statistic for a related-samples t test is 0.5.

Explanation of Solution

Calculation:

The given information is that, $M_D=4,s_{MD}=8$ and consider ${\mu }_D=0$.

Substitute values of, $M_D=4,s_{MD}=8$ and ${\mu }_D=0$ in test statistic formula.

$\begin{array}{c}{t}_{\text{obt}}=\frac{4-0}{8}\\ =\frac{1}{2}\\ =0.5\end{array}$

Hence, the value of the test statistic for a related-samples t test is 0.5.

3.

To determine

Find the value of the test statistic for a related-samples t test.

Answer to Problem 18CAP

The value of the test statistic for a related-samples t test is 4.

Explanation of Solution

Calculation:

The given information is that, $n_D=64,M_D=8,s_D=16$ and consider ${\mu }_D=0$.

Substitute values of, $n_D=64,M_D=8,s_D=16$ and ${\mu }_D=0$ in test statistic formula.

$\begin{array}{c}{t}_{\text{obt}}=\frac{8-0}{\left(\frac{16}{\sqrt{64}}\right)}\\ =\frac{8}{\left(\frac{16}{8}\right)}\\ =\frac{8}{2}\\ =4\end{array}$

Hence, the value of the test statistic for a related-samples t test is 4.

4.

To determine

Find the value of the test statistic for a related-samples t test.

Answer to Problem 18CAP

The value of the test statistic for a related-samples t test is 0.5.

Explanation of Solution

Calculation:

The given information is that, $M_D=8,s_{MD}=16$ and consider ${\mu }_D=0$.

Substitute values of, $M_D=8,s_{MD}=16$ and ${\mu }_D=0$ in test statistic formula

$\begin{array}{c}{t}_{\text{obt}}=\frac{8-0}{16}\\ =\frac{1}{2}\\ =0.5\end{array}$

Hence, the value of the test statistic for a related-samples t test is 0.5.