Question

In a random sample of 1000 persons from a large population, 470 are females. Can it be concluded that males and females are in equal proportion in the population? (use a = 0.05).

Answer 1

Given: n = 1000; x = 470;  P = \(\frac{x}{n}\) = \(\frac{470}{100}\) 0.47 and P₀/P –population proportion = 0.5;

Q₀ = 1 – p₀ = 0.5 [male and female are in equal in proportion]

H₀: Male and female are in equal proportion [P₀ = 0.5]

H₁: Male and female are not in equal proportion [p₀ ≠ 0.5]

under H₀, the test statistic is:-

At α = 0.5 the two tail critical values are ±1.96 Here z_cal lies in A.R. 

∴ H₀ is accepted.

Conclusion: P₀ = 0.5 [male and female are in equal proportion]