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 p1 and p2 be the proportion of all parts from suppliers 1 and 2, respectively, that are defective. Is there evidence of a difference in the proportion of defective parts produced by the two suppliers? To make this determination, you test the hypotheses H0 : p1 = p2 and Ha : p1 ≠ p2. The P-value of your test is

a) 0.1164.

b) 0.0301.

c) 0.0602.

Answer 1

Option C) 0.0602

Explanation:

We are given the following in the question:

`x_1 = 20\\n_1 = 400\\x_2 = 10\\n_2 = 100`

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

`p_1 = (x_1)/(n_1) = (20)/(400) = 0.05\\\\p_2 = (x_2)/(n_2) = (x_2)/(n_2) = (10)/(100)= 0.1`

First, we design the null and the alternate hypothesis

`H_(0): p_1 = p_2\\H_A: p_1 \\eq p_2`

We use Two-tailed z test to perform this hypothesis.

Formula:

`\text{Pooled P} = (x_1+x_2)/(n_1+n_2)\\\\Q = 1 - P\\\\Z_(stat) = \frac{p_1-p_2}{\sqrt{PQ((1)/(n_1) + (1)/(n_2))}}`

Putting all the values, we get,

`\text{Pooled P} = (20+10)/(400+100) = 0.06\\\\Q = 1 - 0.06 = 0.94\\\\Z_(stat) = \frac{0.05-0.1}{\sqrt{0.06* 0.94((1)/(400) + (1)/(100))}} = -1.883`

Now, we calculate the p-value from the table at 0.05 significance level.

P-value = 0.0602

Thus, the correct answer is

Option C) 0.0602