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

Answer:

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))"

$0.05 < p_v <0.1$

Step-by-step explanation:

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

Null hypothesis: $\mu =0$

Alternative hypothesis: $\mu \neq 0$

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))"

$0.05 < p_v <0.1$