Question

Suppose that we are testing H0 : 0 versus H1 : 0 with a sample size of n 10. Calculate bounds on the P-value for the following observed values of the test statistic:

Answer 1

a)
`p_V = 2*P(t_(9) >|2.48|) =0.0349`

We can use the following excel code: "=2*(1-T.DIST(2.48,9,TRUE))"

`0.03 < p_v <0.04`

b)
`p_V = 2*P(t_(9) >|-3.95|)=0.003355`

We can use the following excel code: "=2*(1-T.DIST(3.95,9,TRUE))"

`p_v <0.01`

c)
`p_V = 2*P(t_(9) >|2.69|) =0.02480`

We can use the following excel code: "=2*(1-T.DIST(2.69,9,TRUE))"

`0.01 < p_v <0.03`

d)
`p_V = 2*P(t_(9) >|1.88|) =0.09281`

We can use the following excel code: "=2*(1-T.DIST(1.88,9,TRUE))"

`0.05 < p_v <0.1`

Explanation:

For this case we are testing the following system of hypothesis:

Null hypothesis:
`\mu =0`

Alternative hypothesis:
`\mu \\eq 0`

The sample size is n=10, so then the degrees of freedom are given by:

`df=n-1= 10-1=9`

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|)`

Where
`t_0` represent the calculated or observed statistic.

a) t0= 2.48

`p_V = 2*P(t_(9) >|2.48|) =0.0349`

We can use the following excel code: "=2*(1-T.DIST(2.48,9,TRUE))"

`0.03 < p_v <0.04`

b) t0= -3.95

`p_V = 2*P(t_(9) >|-3.95|)=0.003355`

We can use the following excel code: "=2*(1-T.DIST(3.95,9,TRUE))"

`p_v <0.01`

c) t0=2.69

`p_V = 2*P(t_(9) >|2.69|) =0.02480`

We can use the following excel code: "=2*(1-T.DIST(2.69,9,TRUE))"

`0.01 < p_v <0.03`

d) t0=1.88

`p_V = 2*P(t_(9) >|1.88|) =0.09281`

We can use the following excel code: "=2*(1-T.DIST(1.88,9,TRUE))"

`0.05 < p_v <0.1`