Question

A random sample of 300 circuits generated 13 defectives. Use the data to test the hypothesis Upper H Subscript 0 Baseline colon p equals 0.05 against Use . Find the P-value for the test.

Answer 1

Complete Question

A random sample of 300 circuits generated 13 defectives. a. Use the data to test

`H_o : p = 0.05`

Versus

`H_1 : p \\e 0.05`

Use α = 0.05. Find the P-value for the test

Answer:

The p-value is
`p-value = 0.5949`

Explanation:

From the question we are told that

The sample size is n = 300

The number of defective circuits is k = 13

Generally the sample proportion of defective circuits is mathematically represented as

`\^ p = (k)/(n)`

=>
`\^ p = (13)/(300)`

=>
`\^ p = 0.0433`

Generally the standard Error is mathematically represented as

`SE = \sqrt{(p(1- p))/(n) }`

=>
`SE = \sqrt{(0.05(1- 0.05))/(300) }`

=>
`SE = 0.0126`

Generally the test statistics is mathematically represented as

`z = (\^ p - p )/(SE)`

=>
`z = (0.0433 - 0.05 )/(0.0126)`

=>
`z = -0.5317`

From the z table the area under the normal curve to the left corresponding to -0.5317 is

`(P < -0.5317 ) = 0.29747`

Generally the p-value is mathematically represented as

`p-value = 2 * P(Z < -0.5317 )`

=>
`p-value = 2 * 0.29747`

=>
`p-value = 0.5949`