Answer:
(a) The value of the test statistic is 2.
(b) The <em>p</em>-value of the test is, 0.081.
Step-by-step explanation:
The dependent t-test (also known as the paired t-test or paired-samples t-test) compares the two means of associated groups to conclude if there is a statistically significant difference amid these two means.
We use the paired t-test if we have two measurements on the same item, person or thing.
The hypothesis for the test is defined as:
<em>H₀</em>:
vs. <em>Hₐ</em>:
.
(a)
The t-statistic is given by:
![t=\frac{d}{SD/\sqrt{n}}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bd%7D%7BSD%2F%5Csqrt%7Bn%7D%7D)
Given:
d = 2.2
SD = 3.3
n = 9
Compute the value of <em>t</em> as follows:
![t=\frac{d}{SD/\sqrt{n}}=\frac{2.2}{3.3/\sqrt{9}}=2](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bd%7D%7BSD%2F%5Csqrt%7Bn%7D%7D%3D%5Cfrac%7B2.2%7D%7B3.3%2F%5Csqrt%7B9%7D%7D%3D2)
Thus, the value of the test statistic is 2.
(b)
The level of significance is, <em>α</em> = 0.0403.
Compute the <em>p</em> value of the test statistic as follows:
The test statistic value is, <em>t</em> = 2
The degrees of freedom is, (<em>n</em> - 1) = 9 - 1 = 8.
Use a <em>t</em>-table for the <em>p</em>-value.
![p-value=0.081](https://tex.z-dn.net/?f=p-value%3D0.081)
Conclusion:
As the <em>p</em>-value = 0.081 > <em>α</em> = 0.0403, the null hypothesis was failed to be rejected.