Question

A machine produced 25 defective articles in a batch of 400. After over hauling it produced 15 defectives in a batch of 200. Test at 1% level of significance whether there is a reduction of defective articles after overhauling.

Answer 1

n₁ = 400, x₁ = 25 

∴ P₁ = \(\frac{x_1}{n_1}\) = \(\frac{25}{400}\) = 0.0625.

n₂ = 200 x₂ = 15 

∴P₂ = \(\frac{x_2}{n_2}\) = \(\frac{15}{200}\)= 0.075

H₀ : The proportion of defective articles before and after overhauling is the same (i.e H₀ : p₁ = p₂)

H₁ : The proportion of defective articles are more before overhauling 

(i.e H₁ : p₁ > p₂) { Right upprt Tailed test}

The test statistic is

∴ Zeal = -0.576 

At α = 1 % the upper/right tail critical values K = 2.33 

Here Z_cal = -0.576 is in acceptance region/ Z_cal 

∴ H₀ is accepted. 

Conclusion : The proportion of defective articles before and after .over hauling is same.