Question

Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60 Minutes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Lucy plans to test this hypothesis using a random sample of 100 from each audience. Her alternate hypothesis is ____________.

Answer 1

Answer:

Alternative hypothesis:$\mu_1 -\mu_2 \neq 0$

Or in the alternative way would be:

 Alternative hypothesis:$\mu_1 \neq \mu_2$

Step-by-step explanation:

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

On this case the claim that they want to test is: "The means for the two groups (American Idol and 60 Minutes) is the same". So we want to check if we have significant differences between the two means, so this needs to be on the alternative hypothesis and on the null hypothesis we need to have the complement of the alternative hypothesis.

Null hypothesis:$\mu_1 -\mu_2 = 0$

This null hypothesis can be expressed like this:

Null hypothesis:$\mu_1 = \mu_2$

Alternative hypothesis:$\mu_1 -\mu_2 \neq 0$

Or in the alternative way would be:

Alternative hypothesis:$\mu_1 \neq \mu_2$