Question

A sample of 300 people in country A showed 12% were left-handed, while a sample of 250 people in country B showed 10% were left-handed. Is there enough evidence to conclude the proportion of left-handedness is different in these countries? Use α = 0.05.

Answer 1

Given that,

For Country A : n1 = 300 and

For Country B : n2 = 250 and

Pooled proportion is,

The null and alternative hypotheses are,

H0 : p1 = p2

Ha : p1 ≠ p2

Test statistic is,

=> Test statistic = Z = 0.74

p-value = 2 * P(Z > 0.74)

=> p-value = 2 * [ 1 - P(Z < 0.74) ]

=> p-value = 2 * [ 1 - 0.7704 ]

=> p-value = 2 * 0.2296

=> p-value = 0.4592

Since, p-value is greater than significance level of 0.05, we fail to Reject H0.

Conclusion : There is not enough evidence to conclude the proportion of left-handedness is different in these countries.