Question

$H_2*{\mu }_1\ne {\mu }_2$

Short answer

Since the value of test statistics is fall in the accepted region. Thus, the null hypothesis is not rejected.

Step-by-step solution

Given information

The hypothesis is

$$\begin{gathered} H_0:{\mu }_1={\mu }_2, \\ {H}_a:{\mu }_1={\mu }_2 \end{gathered}$$

and the level of significance is 0

Explanation

Let's compute the sample mean as follow

$\overline{d}=\frac{\sum d}{n}$

$=\frac{7}{8}$

$=0.875$

Calculate the value of standard deviation is,

$s_d=\sqrt{\frac{\sum d_i^2-\frac{{\left(\sum d_i\right)}^2}{n}}{n-1}}$

$$\begin{gathered} =\sqrt{\frac{47-\frac{(7{)}^2}{8}}{8-1}} \\ =2.4165 \end{gathered}$$

The test statistics are,

$t=\frac{\overline{d}}{\frac{s_d}{\sqrt{n}}}$

Substitute the given values in the above equation.

$z=\frac{0.875}{\frac{2.4165}{\sqrt{5}}}$

$=1.024$

The nvalue of degree of freedom is,

$$\begin{gathered} dof=n-1 \\ =8-1 \\ =7 \end{gathered}$$

The critical value for a level of significance of $0.1$is $1.895$.