Respuesta :
Answer:
a) The degrees of freedom are given by:
[tex]df = 15[/tex]
And the rejection region is [tex]t_{\alpha}<3.733[/tex]
And the significance level would be:
[tex]P(t_{15} >3.733) =0.001[/tex]
b) The degrees of freedom are given by:
[tex]df = 24-1=23[/tex]
And the rejection region is [tex]t_{\alpha} <-2.5[/tex]
And the significance level would be:
[tex]P(t_{23} <-2.5) =0.0099 \approx 0.01[/tex]
c) The degrees of freedom are given by:
[tex]df = 31-1=30[/tex]
And the rejection region is [tex]t_{\alpha} <-1.697[/tex] or [tex]t_{\alpha} >1.697[/tex]
And the significance level would be:
[tex]2*P(t_{30} <-1.697) =0.10[/tex]
Step-by-step explanation:
Part a
We have the following system of hypothesis:
Null hypothesis: [tex]\mu \leq \mu_0 [/tex]
Alternative hypothesis: [tex]\mu > \mu_0 [/tex]
The degrees of freedom are given by:
[tex]df = 15[/tex]
And the rejection region is [tex]t_{\alpha}<3.733[/tex]
And the significance level would be:
[tex]P(t_{15} >3.733) =0.001[/tex]
Part b
We have the following system of hypothesis:
Null hypothesis: [tex]\mu \geq \mu_0 [/tex]
Alternative hypothesis: [tex]\mu < \mu_0 [/tex]
The degrees of freedom are given by:
[tex]df = 24-1=23[/tex]
And the rejection region is [tex]t_{\alpha} <-2.5[/tex]
And the significance level would be:
[tex]P(t_{23} <-2.5) =0.0099 \approx 0.01[/tex]
Part c
We have the following system of hypothesis:
Null hypothesis: [tex]\mu = \mu_0 [/tex]
Alternative hypothesis: [tex]\mu \neq \mu_o[/tex]
The degrees of freedom are given by:
[tex]df = 31-1=30[/tex]
And the rejection region is [tex]t_{\alpha} <-1.697[/tex] or [tex]t_{\alpha} >1.697[/tex]
And the significance level would be:
[tex]2*P(t_{30} <-1.697) =0.10[/tex]
