Question

uppose that 500 parts are tested in manufacturing and 10 are rejected. Test the hypothesis Upper H Subscript 0 Baseline colon p equals 0.03 against Upper H Subscript 1 Baseline colon p less-than 0.03 at . Find the P-value.

Answer 1

The value is
`p-value = 0.094963`

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
`H_o : p = 0.03`

The alternative hypothesis is
`H_1 : p < 0.03`

Generally the sample proportion is mathematically represented as

`\^ p = (10)/(500)`

=>
`\^ p = 0.02`

Generally the test statistics is mathematically represented as

`z = \frac{\^ p - p }{ \sqrt{(p (1-p))/(n) } }`

=>
`z = \frac{0.02 - 0.03 }{ \sqrt{( 0.03 (1-0.03))/(500) } }`

=>
`z = -1.31080`

From the z table the probability of (Z < -1.31080) is

`p-value = P(Z < -1.31080) = 0.094963`