Question

The operations manager of a sales company wants to see whether there is a significant difference in the ages of male and female customers. He selected a sample of 35 samples for each group. The ages are shown in the table below: Male Female x̄1 = 27.3 x̄ 2 = 28 σ1 = 2.4 σ2 = 3.1 n1 = 35 n2 = 35 At a = 0.05, decide if there is enough evidence to reject the claim of no difference in the ages of the two groups. Solution:

Answer 1

Since sample standard deviations are not equal, t-test unequal variances is used. Similarly, since $\sigma$s are given, (population standard deviations), z is used.

$H0:\mu_1=\mu_2$

$Ha:\mu_1\ne\mu_2$

$\displaystyle{z}=\frac{(\overline{x}_1-\overline{x}_2)-(\mu_1-\mu_2)}{\sqrt{\frac{(\sigma_1)^2}{n_1}+\frac{(\sigma_2)^2}{n_2}}}$

$\displaystyle{z}=\frac{27.3-28}{\sqrt{\frac{2.4^2}{35}+\frac{3.1^2}{35}}}=-1.056$

$CV=Z_{0.025}=\pm1.96$

Since$|z|<|CV|$ we fail to reject the null hypothesis and conclude that there is no significant evidence to reject the claim that there is no difference in ages between males and females.