Answer:
The value is [tex]p-value = 0.094963[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 500
The number of rejected parts is k = 10
The null hypothesis is [tex]H_o : p = 0.03[/tex]
The alternative hypothesis is [tex]H_1 : p < 0.03[/tex]
Generally the sample proportion is mathematically represented as
[tex]\^ p = \frac{10}{500}[/tex]
=> [tex]\^ p = 0.02[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\^ p - p }{ \sqrt{\frac{p (1-p)}{n} } }[/tex]
=> [tex]z = \frac{0.02 - 0.03 }{ \sqrt{\frac{ 0.03 (1-0.03)}{500} } }[/tex]
=> [tex]z = -1.31080[/tex]
From the z table the probability of (Z < -1.31080) is
[tex]p-value = P(Z < -1.31080) = 0.094963[/tex]
