Question

In a village, 200 out of 300 men are smokers. Does this data support the argument that majority of men in the village are smokers ?

Answer 1

Given : n = 300 ; x = 200

∴ p = \(\frac{x}{n}\) = \(\frac{200}{300}\) = 0.67

H₀: Proportion of smokers is 0.5

(i.e., H₀: P₀ = 0.5) .

H₁ : Proportion of smokers is more than 0.5 

(i.e., H₁ : P₀ > 0.5) {upper tail test} 

Here it is assumed that proportion of smokers and non-smokers are equal. 

Therefore P₀ = 0.5.

The test statistic is :

At α = 5% the upper tail critical value is K = 1.645. 

Here Z_cal > K. 

∴ H₀ is rejected and H₁ is accepted. 

Conclusion : Majority of men in the village are smokers i.e., proportion of smokers is more than 0.5.