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

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)`

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 \\eq m`

The statistic is given by

`z=(\bar X-\mu_o)/((\sigma)/(√(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))"