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. If population 1 is defined as men and population 2 is defined as women the correct hypotheses are

Answer 1

See below

Explanation:

Let
`\bf \mu_1` and
`\bf\mu_2` be the average age of population 1 (men) and 2 (women) respectively.

The correct hypothesis would be

Null Hypothesis

`\bf H_0: \mu_1=\mu_2`

Alternative Hypothesis

`\bf H_a: \mu_1>\mu_2`

It is worth noticing that in order to be able to make the hypothesis test it is necessary to know:

• The approximate data distribution of ages from population 1 and 2 (which is oftentimes a Normal distribution in these kind of sociological studies)
• The standard deviation of population 1 and 2. Since this is almost always impossible to determine in very large populations, then an estimation of the standard deviation together with the sample size used to determine it is required.
• The level of confidence required to asses the hypothesis. The most common ones are 90%, 95%and 99%