Newly purchased automobile tires of a certain type are supposed to be filled to a pressure of 30 psi. Let μ denote the true average pressure. Find the P-value associated with each of the following given z statistic values for testing H0: μ = 30 versus Ha: μ 30 when σ is known. (Give the answers to four decimal places.)

Answers

Answer 1

Complete Question

Newly purchased automobile tires of a certain type are supposed to be filled to a pressure of 30 psi. Let μ denote the true average pressure. Find the P-value associated with each of the following given z statistic values for testing H0: μ = 30 versus Ha: μ 30 when σ is known. (Give the answers to four decimal places.)

calculate for each

(a) z = 2.30

(b) z = -1.7

Answer:

a

[tex]p-value = 0.021448[/tex]

b

[tex]p-value = 0.08913[/tex]

Step-by-step explanation:

From the question we are told that

   The population mean is [tex]\mu = 30 \ psi[/tex]

   The null hypothesis [tex]H_o : \mu = 30[/tex]

    The alternative hypothesis is  [tex]H_a : \mu \ne 30[/tex]

Considering question a  

 Here  the test statistics is (a) z = 2.30  

 From the z table  the probability of  (Z >  2.30)  is  

      [tex]P(Z > 2.30 ) = 0.010724[/tex]

Generally the p-value is mathematically represented as

      [tex]p-value = 2 * P(Z > 2.30 )[/tex]

=>   [tex]p-value = 2 * 0.010724[/tex]

=>   [tex]p-value = 0.021448[/tex]

Considering question b

 Here  the test statistics is (a) z = -1.7

 From the z table  the probability of  (Z <  -1.7)  is  

      [tex]P(Z < -1.7 ) = 0.044565[/tex]

Generally the p-value is mathematically represented as

      [tex]p-value = 2 * P(Z < -1.70 )[/tex]

=>   [tex]p-value = 2 * 0.044565[/tex]

=>   [tex]p-value = 0.08913[/tex]


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