Question

400 products on line A are examined and 40% are found to be defective, 100 products on line B are examined and 20% are found to be defective. What is the appropriate test statistic?

Answer 1

Solution :

Two proportions z test

Given that,

n₁ = 400

₁ = 40% = 0.40

x₁ = 400 * 0.40 = 160

n₂ =100

₂ = 20% = 0.20

x₂ = 100 * 0.20 = 20

Let be the pooled proportion.

= (x1 +x2)/(n1 + n2) = (160 + 20)/(400 + 100) = 0.36

1 - = 1 - 0..36 = 0.64

The test statistic z is

z =  

    = (0.40 - 0.20)/[0.36 *0.64*((1/400)+(1/100))]

= 3.73