Answer:
a) ![p_V = 2*P(t_{9} >|2.48|) =0.0349](https://tex.z-dn.net/?f=%20p_V%20%3D%202%2AP%28t_%7B9%7D%20%3E%7C2.48%7C%29%20%3D0.0349%20)
We can use the following excel code: "=2*(1-T.DIST(2.48,9,TRUE))"
![0.03 < p_v](https://tex.z-dn.net/?f=%200.03%20%3C%20p_v%20%3C0.04)
b) ![p_V = 2*P(t_{9} >|-3.95|)=0.003355](https://tex.z-dn.net/?f=%20p_V%20%3D%202%2AP%28t_%7B9%7D%20%3E%7C-3.95%7C%29%3D0.003355%20)
We can use the following excel code: "=2*(1-T.DIST(3.95,9,TRUE))"
![p_v](https://tex.z-dn.net/?f=%20p_v%20%3C0.01)
c) ![p_V = 2*P(t_{9} >|2.69|) =0.02480](https://tex.z-dn.net/?f=%20p_V%20%3D%202%2AP%28t_%7B9%7D%20%3E%7C2.69%7C%29%20%3D0.02480%20)
We can use the following excel code: "=2*(1-T.DIST(2.69,9,TRUE))"
![0.01 < p_v](https://tex.z-dn.net/?f=%200.01%20%3C%20p_v%20%3C0.03)
d) ![p_V = 2*P(t_{9} >|1.88|) =0.09281](https://tex.z-dn.net/?f=%20p_V%20%3D%202%2AP%28t_%7B9%7D%20%3E%7C1.88%7C%29%20%3D0.09281)
We can use the following excel code: "=2*(1-T.DIST(1.88,9,TRUE))"
![0.05 < p_v](https://tex.z-dn.net/?f=%200.05%20%3C%20p_v%20%3C0.1)
Step-by-step explanation:
For this case we are testing the following system of hypothesis:
Null hypothesis: ![\mu =0](https://tex.z-dn.net/?f=%5Cmu%20%3D0)
Alternative hypothesis: ![\mu \neq 0](https://tex.z-dn.net/?f=%5Cmu%20%5Cneq%200)
The sample size is n=10, so then the degrees of freedom are given by:
![df=n-1= 10-1=9](https://tex.z-dn.net/?f=%20df%3Dn-1%3D%2010-1%3D9)
In order to calculate the p value we can use the fact that we are conducting a bilateral test so then the p value is given by:
![p_V = 2*P(t_{9} >|t_0|)](https://tex.z-dn.net/?f=%20p_V%20%3D%202%2AP%28t_%7B9%7D%20%3E%7Ct_0%7C%29%20)
Where
represent the calculated or observed statistic.
a) t0= 2.48
![p_V = 2*P(t_{9} >|2.48|) =0.0349](https://tex.z-dn.net/?f=%20p_V%20%3D%202%2AP%28t_%7B9%7D%20%3E%7C2.48%7C%29%20%3D0.0349%20)
We can use the following excel code: "=2*(1-T.DIST(2.48,9,TRUE))"
![0.03 < p_v](https://tex.z-dn.net/?f=%200.03%20%3C%20p_v%20%3C0.04)
b) t0= -3.95
![p_V = 2*P(t_{9} >|-3.95|)=0.003355](https://tex.z-dn.net/?f=%20p_V%20%3D%202%2AP%28t_%7B9%7D%20%3E%7C-3.95%7C%29%3D0.003355%20)
We can use the following excel code: "=2*(1-T.DIST(3.95,9,TRUE))"
![p_v](https://tex.z-dn.net/?f=%20p_v%20%3C0.01)
c) t0=2.69
![p_V = 2*P(t_{9} >|2.69|) =0.02480](https://tex.z-dn.net/?f=%20p_V%20%3D%202%2AP%28t_%7B9%7D%20%3E%7C2.69%7C%29%20%3D0.02480%20)
We can use the following excel code: "=2*(1-T.DIST(2.69,9,TRUE))"
![0.01 < p_v](https://tex.z-dn.net/?f=%200.01%20%3C%20p_v%20%3C0.03)
d) t0=1.88
![p_V = 2*P(t_{9} >|1.88|) =0.09281](https://tex.z-dn.net/?f=%20p_V%20%3D%202%2AP%28t_%7B9%7D%20%3E%7C1.88%7C%29%20%3D0.09281)
We can use the following excel code: "=2*(1-T.DIST(1.88,9,TRUE))"
![0.05 < p_v](https://tex.z-dn.net/?f=%200.05%20%3C%20p_v%20%3C0.1)