Question

A manufacturer claims that less than 2% of his products are defective. A retailer buys a batch of 250 articles from the manufacturer and find that 13 are defectives. Test at 1% level of significance that whether the manufacturer’s claim is justifiable.

Answer 1

Given P₀ = 0.02, 

n = 250, x= 13, α = 1%

∴ P = \(\frac{x}{n}\) = \(\frac{13}{250}\) = 0.052; 

Q₀ = 1 – p₀ =1 – 0.02 = 05.98

H₀ : proportion of defective products are 2% 

(i.e. H₀: P₀ = 2% = 0.02) 

H₁ : proportion of defective products are less than 2%…… 

(i.e H <sub.1 : p₀ < 2%)

(lower tail test)

Z_cal =3.636

At α = 5% the lower tail critical value – k = – 2.33

Here Z_cal > – k /Z_cal lies in (AR) acceptance region. 

∴ H₀ is accepted

Conclusion : proportion of defective products are 0.02 or 2%.