Question

1. Is there sufficient evidence to conclude that there is a difference in the mean age of male customers vs female customers?

DATA

Equal variances assumed

F= 1.572

Sig=.210

t= .370

df= 4998

Sig. (2- tailed)= .712

Mean difference= .185

Std. Error difference= .501

Lower= -.797

Upper= 1.167 95% confidence Interval

Equal variances not assumed

t= .370

df= 4992. 696

Sig. (2-tailed)= .712

Mean difference= .185

Std. Error difference= .501

Lower= .797

Upper= 1.167

a. should they reject or retain? give numerical justification

b. calculate the effect size

c. interpret the effect size in the context of the situation

Answer 1

First we need to check the variances are equal or different using F test

Given : p value for F test = 0.210

Since P value is greater than 0.05 , we fail to reject H₀: σ²₁ = σ²₂ , so we can conclude that the variances are equal.

So we have to look at the results for Equal variances assumed test for difference between two means.

Claim :  There is a difference in the mean age of male customers vs female customers

H₀: µ₁ = µ₂    vs H_a: µ₁ ≠ µ₂   

Given : t = .370 , Sig. (2- tailed)= .712

As p-value is greater than 0.05 , we retain the null hypothesis H₀

Conclusion : There is no significant evidence that the mean age of male customers vs female customers are different.

b) effect size = =   = 0.00003

c) The effect size is approximately 0 , it means that the difference between mean age of male customers vs female customers is approximately equal to 0

Or 0% of the variance in age is explained by the gender .