Question

In an accelerated failure test, components are operated under extreme conditions so that a substantial number will fail in a rather short time. In such a test involving two types of microchips, 620 chips manufactured by an existing process were tested, and 125 of them failed. Then, 820 chips manufactured by a new process were tested, and 130 of them failed. Find a 90% confidence interval for the difference between the proportions of failures for chips manufactured by the two processes. (Round the final answers to four decimal places.)

The 90% confidence interval is ( . , ).

Answer 1

Solution :

Given that,

n₁ = 620

x₁ = 125

₁ = x₁ / n₁ = 0.202

n₂ = 820

x₂ = 130

₂ = x₂ / n₂ = 0.159

1) Point estimate of difference between two proportions

= ₁ -  ₂

= 0.202 - 0.159

= 0.043

2)

Our aim is to construct 90% confidence interval.

c = 0.90

= 1- c = 1- 0.90 = 0.10

  /2 = 0.10 2 = 0.05 and 1- /2 = 0.950

= 1.645 (use z table)

Margin of error =   *

=  

= 0.0340

3) Required interval is

Point estimate   Margin of error

0.043   0.037734

(0.43 - 0.0340 , -0.43 +  0.0340)

( 0.0090, 0.0770)