A recent study focused on the amount of money single men and

A recent study focused on the amount of money single men and women save monthly. The information is summarized below. Assume that the population standard deviations are equal.

At the 0.04 significance level, do women save more money than men? What is the value of the critical value for this hypothesis test?

Solution

Standard error, SE = sqrt[(s₁²/n₁) + (s₂²/n₂)] = sqrt[(93²/38) + (70²/51)] = 18.029

Degrees of freedom, DF = (s₁²/n₁ + s₂²/n₂)² / { [ (s₁² / n₁)² / (n₁ - 1) ] + [ (s₂² / n₂)² / (n₂ - 1) ] }

                                    = (93²/38 +70²/51)² / { [ (93² / 38)² / (38 - 1) ] + [ (70² / 51)² / (51 - 1) ] } = 66.11

test statistics, t = [ (x₁ - x₂) - d ] / SE = (502-473)/18.029 =1.60852

Critical value for the test, (for 0.04 level , one sided, DF = 66) = 1.77

since test statistics is less than critical value, women do not save significently more than men.