Question

Among 40 randomly selected people from urban area, 5 are interested in viewing football match. Among 50 randomly selected people from rural area, 4 are interested in viewing football match. Test st 5% level of significance, whether the proportion of viewers in urban and rural areas are the same.

Answer 1

n₁ = 40 ; x₁ = 5, 

∴ p₁ = \(\frac{x_1}{n_1}\) = \(\frac{5}{40}\)= 0.125

n₂ = 50: x₂ = 4 

∴P₂ =\(\frac{x_1}{n_1}\)= \(\frac{4}{40}\) = 0.08

H₀: The proportion of viewers in urban and rural areas are same.

 (i e., H₀: P₁= P₂) 

H₁ : The proportion of viewers in urban and rural areas are not same, 

(i.e., H₁ : P₁ ≠ P₂) {two Tailed test}.

The test Statistic is

Z_cal = 0.7075 

At α = 5%, the two tail critical values are -K₁= -1.96 and K₂ 

= 1.96. 

Here Zeal = 0.7075 is in acceptance region/ Z_cal is in between K₁ and K₂ 

∴ H₀ is accepted. 

Conclusion : The proportion of viewers of football match in urban and rural areas are the same.