Respuesta :
Answer:
[tex]p_v =P(t_{(n-1)}>t_{calculated}) =0.0601[/tex]
The p value on this case is given by the problem.
If we compare the p value with a significance level assumed [tex]\alpha=0.05[/tex], we see that [tex]p_v > \alpha[/tex] and we can conclude that we FAIL to reject the null hypothesis that the difference mean between after and before is less or equal than 0.
Step-by-step explanation:
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.
Let put some notation
x=test value before , y = test value after
The system of hypothesis for this case are:
Null hypothesis: [tex]\mu_y- \mu_x \leq 0[/tex]
Alternative hypothesis: [tex]\mu_y -\mu_x >0[/tex]
The first step is calculate the difference [tex]d_i=y_i-x_i[/tex]
The second step is calculate the mean difference
[tex]\bar d= \frac{\sum_{i=1}^n d_i}{n}[/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}[/tex]
The 4 step is calculate the statistic given by :
[tex]t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=t_{calculated}[/tex]
The next step is calculate the degrees of freedom given by:
[tex]df=n-1[/tex]
Now we can calculate the p value, since we have a right tailed test the p value is given by:
[tex]p_v =P(t_{(n-1)}>t_{calculated}) =0.0601[/tex]
The p value on this case is given by the problem.
If we compare the p value with a significance level assumed [tex]\alpha=0.05[/tex], we see that [tex]p_v > \alpha[/tex] and we can conclude that we FAIL to reject the null hypothesis that the difference mean between after and before is less or equal than 0.
Considering the p-value of the test, it is found that we do not reject the null hypothesis [tex]H_0: \mu_D > 0[/tex].
What is the decision rule for a hypothesis test considering the p-value?
- If the p-value is greater than the significance level, we do not reject the null hypothesis.
- If the p-value is less than the significance level, we reject the null hypothesis.
In this problem, considering the standard significance level of 0.05 and the p-value of 0.0601 > 0.05, we do not reject the null hypothesis [tex]H_0: \mu_D > 0[/tex].
More can be learned about p-values at https://brainly.com/question/16313918
