Question

A manufacturer receives parts from two suppliers. An SRS of 400 parts from supplier 1 finds 20 defective; an SRS of 100 parts from supplier 2 finds 10 defective. Let p 1 p1 and p 2 p2 be the proportion of all parts from suppliers 1 and 2, respectively, that are defective. The manufacturer wants to know if there is evidence of a difference in the proportion of defective parts produced by the two suppliers. To make this determination, you test the hypotheses H 0 : p 1 = p 2 H0:p1=p2 and H a : p 1 ≠ p 2 .

Answer 1

Since p >0.05 at 5% level we find that there is no evidence of a difference in the proportion of defective parts produced by the two suppliers

Explanation:

Given that a manufacturer receives parts from two suppliers. An SRS of 400 parts from supplier 1 finds 20 defective; an SRS of 100 parts from supplier 2 finds 10 defective.

Let p 1 p1 and p 2 p2 be the proportion of all parts from suppliers 1 and 2, respectively, that are defective.

`H 0 : p 1 = p 2 \\H a : p 1 \\eq  p 2 .`

(two tailed test )

Sample I II total

N 400 100 500

x 20 10 30

p 0.05 0.10 0.06

`Std error =\sqrt{\bar p(1- \bar p)((1)/(n_1) +(1)/(n_2) )}  \\=0.0266`

Z= -1.8831

p value = 0.0601

Since p >0.05 at 5% level we find that there is no evidence of a difference in the proportion of defective parts produced by the two suppliers