Question

The federal government would like to test the hypothesis that the average age of men filing for Social Security is higher than the average age of women set using α =  0.05 with the following data:

	Men	Women
Sample mean	64.5 years	63.6 years
Sample size	35	39
Population standard deviation	3.0 years	3.5 years

If Population 1 is defined as men and Population 2 is defined as women, the correct hypothesis statement for this hypothesis test would be

		H0: μ1 - μ2 = 0; H1: μ1 - μ2 < 0
		H0: μ1 - μ2 = 0; H1: μ1 - μ2 ≠ 0
		H0: μ1 - μ2 =0; H1: μ1 - μ2 > 0
		H0 :μ2 - μ1 = 0; H1: μ2 - μ1 > 0

Answer 1

First consider the given facts.

Population 1 is considered as men, so, n₁=35 $\mu _{1}$ =64.5 $\sigma _{1}$ =3

Population 2 is considered as women, so, n₂=39  $\mu _{2}$=63.6 $\sigma _{2}$ =3.5

Since both sample sizes are greater than 30 Z-test wil be appropiate .

Then the research question for such a test would be, 'Is the average age of men filing for social security is higher than the average age of women'.

Then the alternative hypothesis is H₁: $\mu _{1}$ >$\mu _{2}$  (which is of the form $\mu _{1}$ -$\mu _{2}$>0 )

Therefore the correct hypothesis statement for the hypothesis test would be option 3, i.e,

H_{0 :} $\mu _{1}$ - $\mu _{2}$ =0

H₁: $\mu _{1}$ - $\mu _{2}$ >0 .