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

 

                          $H_1 : p \ne 0.05$

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

   

Answer:

The  p-value is  $p-value = 0.5949$        

Step-by-step 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

        $\^ p = \frac{k}{n}$

=>     $\^ p = \frac{13}{300}$

=>     $\^ p = 0.0433$

Generally the standard Error is mathematically represented as

       $SE = \sqrt{\frac{p(1- p)}{n} }$

=>     $SE = \sqrt{\frac{0.05(1- 0.05)}{300} }$

=>     $SE = 0.0126$

Generally the test statistics is mathematically represented as

       $z = \frac{\^ p - p }{SE}$

=>     $z = \frac{0.0433 - 0.05 }{0.0126}$

=>     $z = -0.5317$

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

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

=>     $p-value = 2 * 0.29747$

=>     $p-value = 0.5949$