Respuesta :
Answer:
d: 2, 4, -6, 0, -1, -5, 0, 1
The second step is calculate the mean difference
[tex]\bar d= \frac{\sum_{i=1}^n d_i}{n}= \frac{29}{8}=-0.625[/tex]
The third step would be calculate the standard deviation for the differences, and we got:
[tex]s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =3.378[/tex]
The next step is calculate the statistic given by :
[tex]t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-0.625 -0}{\frac{3.378}{\sqrt{8}}}=-0.523[/tex]
And the correct option would be:
a. t = -0.523
Step-by-step explanation:
We assume the following notation:
x=test value after , y = test value before
x: 34 39 28 33 27 23 35 33
y: 32 35 34 33 28 28 35 32
The system of hypothesis for this case is given by:
Null hypothesis: [tex]\mu_y- \mu_x = 0[/tex]
Alternative hypothesis: [tex]\mu_y -\mu_x \neq 0[/tex]
The first step is calculate the difference [tex]d_i=y_i-x_i[/tex] and we obtain this:
d: 2, 4, -6, 0, -1, -5, 0, 1
The second step is calculate the mean difference
[tex]\bar d= \frac{\sum_{i=1}^n d_i}{n}= \frac{29}{8}=-0.625[/tex]
The third step would be calculate the standard deviation for the differences, and we got:
[tex]s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =3.378[/tex]
The next step is calculate the statistic given by :
[tex]t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-0.625 -0}{\frac{3.378}{\sqrt{8}}}=-0.523[/tex]
And the correct option would be:
a. t = -0.523
