Question

Newly purchased tires of a particular type are supposed to be filled to a pressure of 30 psi. Let μ denote the true average pressure. A test is to be carried out to decide whether μ differs from the target value. Determine the P-value for each of the following z test statistic values. (Round your answers to four decimal places.)

Answer 1

Answer:

a) $p_v= 2*P(Z>2.10) = 0.0357$

b) $p_v= 2*P(Z<-1.75) = 0.0801$

c) $p_v= 2*P(Z<-0.55) = 0.5823$

d) $p_v= 2*P(Z>1.41) = 0.1585$

e) $p_v= 2*P(Z<-5.3) = 1.158x10^{-7}$

Step-by-step explanation:

Newly purchased tires of a particular type are supposed to be filled to a pressure of 30 psi. Let m denote the true average pressure. A test is to be carried out to decide whether m differs from the target value. Determine the P-value for each of the following z test statistic values.

System of hypothesis

We need to conduct a hypothesis in order to check if the true mean is different from m :    

Null hypothesis:$\mu =m$    

Alternative hypothesis:$\mu \neq m$    

The statistic is given by

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)    

a. 2.10

Since is a bilateral test the p value is given by:

$p_v= 2*P(Z>2.10) = 0.0357$

And we can use the following excel code:

"=2*(1-NORM.DIST(2.1,0,1,TRUE))"

b. -1.75

Since is a bilateral test the p value is given by:

$p_v= 2*P(Z<-1.75) = 0.0801$

And we can use the following excel code:

"=2*(NORM.DIST(-1.75,0,1,TRUE))"

c. -.55

Since is a bilateral test the p value is given by:

$p_v= 2*P(Z<-0.55) = 0.5823$

And we can use the following excel code:

"=2*(NORM.DIST(-0.55,0,1,TRUE))"

d. 1.41

Since is a bilateral test the p value is given by:

$p_v= 2*P(Z>1.41) = 0.1585$

And we can use the following excel code:

"=2*(1-NORM.DIST(1.41,0,1,TRUE))"

e. -5.3

Since is a bilateral test the p value is given by:

$p_v= 2*P(Z<-5.3) = 1.158x10^{-7}$

And we can use the following excel code:

"=2*(NORM.DIST(-5.3,0,1,TRUE))"