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.)

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

$p-value = 0.021448$

b

$p-value = 0.08913$

Step-by-step explanation:

From the question we are told that

   The population mean is $\mu = 30 \ psi$

   The null hypothesis $H_o : \mu = 30$

    The alternative hypothesis is  $H_a : \mu \ne 30$

Considering question a  

 Here  the test statistics is (a) z = 2.30  

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

      $P(Z > 2.30 ) = 0.010724$

Generally the p-value is mathematically represented as

      $p-value = 2 * P(Z > 2.30 )$

=>   $p-value = 2 * 0.010724$

=>   $p-value = 0.021448$

Considering question b

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

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

      $P(Z < -1.7 ) = 0.044565$

Generally the p-value is mathematically represented as

      $p-value = 2 * P(Z < -1.70 )$

=>   $p-value = 2 * 0.044565$

=>   $p-value = 0.08913$