Question

1. Suppose we have the following information on hourly wages for men and women:

Men                                         Women

n₁ = 200                                   n₂ = 100

_                                              _

X₁ = $48                                  X₂ = $45

σ₁ = $20                                  σ₂ = $15

Using a 0.05 level of significance, test the claim that average wages for men exceeds average wages for women in the population.

Answer 1

H0: 1 = 2

Ha: 1 > 2

Test statistics

z = (1 - 2) / sqrt [ 1 / n1 + 2 / n2 ]

= (48 - 45) / sqrt [ 20² / 200 + 15² / 100 ]

= 1.46

This is test statistics value.

From Z table,

z-critical value at 0.05 significance level = 1.645

Since test statistics < 1.645, fail to reject H0.

We conclude that, we do not have sufficient evidence to support the claim that average wages for

men exceeds average wages for women in the population.