Respuesta :
Answer:
a) The critical value on this case would be [tex]t_{crit}=1.325[/tex]
b) The critical value on this case would be [tex]t_{crit}=-1.345[/tex]
c) The critical values on this case would be [tex]t_{crit}=\pm 2.201[/tex]
Step-by-step explanation:
Part a
The system of hypothesis on this case would be:
Null hypothesis: [tex]\mu \leq \mu_0[/tex]
Alternative hypothesis: [tex]\mu > \mu_0[/tex]
Where [tex]\mu_0[/tex] is the value that we want to test.
In order to find the critical value we need to find first the degrees of freedom, on this case that is given df=20. Since its an upper tailed test we need to find a value a such that:
[tex]P(t_{20}>a) = 0.1[/tex]
And we can use excel in order to find this value with this function: "=T.INV(0.9,20)". The 0.9 is because we have 0.9 of the area on the left tail and 0.1 on the right.
The critical value on this case would be [tex]t_{crit}=1.325[/tex]
Part b
The system of hypothesis on this case would be:
Null hypothesis: [tex]\mu \geq \mu_0[/tex]
Alternative hypothesis: [tex]\mu < \mu_0[/tex]
Where [tex]\mu_0[/tex] is the value that we want to test.
In order to find the critical value we need to find first the degrees of freedom, given by:
[tex]df=n-1=15-1=14[/tex]
Since its an lower tailed test we need to find b value a such that:
[tex]P(t_{14}<b) = 0.1[/tex]
And we can use excel in order to find this value with this function: "=T.INV(0.1,14)". The 0.1 is because we have 0.1 of the area accumulated on the left of the distribution.
The critical value on this case would be [tex]t_{crit}=-1.345[/tex]
Part c
The system of hypothesis on this case would be:
Null hypothesis: [tex]\mu = \mu_0[/tex]
Alternative hypothesis: [tex]\mu \neq \mu_0[/tex]
Where [tex]\mu_0[/tex] is the value that we want to test.
In order to find the critical value we need to find first the degrees of freedom, given by:
[tex]df=n-1=12-1=11[/tex]
Since its a two tailed test we need to find c value a such that:
[tex]P(t_{11}>c) = 0.025[/tex] or [tex]P(t_{11}<-c) = 0.025[/tex]
And we can use excel in order to find this value with this function: "=T.INV(0.025,11)". The 0.025 is because we have 0.025 of the area on each tail.
The critical values on this case would be [tex]t_{crit}=\pm 2.201[/tex]
