Question

When conducting a test for the difference of means for two independent populations x1 and x2, what alternate hypothesis would indicate that the mean of the x2 population is larger than that of the x1 population? Express the alternate hypothesis in two ways.

Answer 1

Answer:

So the correct system of hypothesis for this case would be:

Null hypothesis: $\mu_{2} - \mu_{1}\leq 0$

Alternative hypothesis: $\mu_{2} - \mu_{1} > 0$

On the other way would be:

Null hypothesis: $\mu_{2} \leq \mu_{1}$

Alternative hypothesis: $\mu_{2} > \mu_{1}$

Step-by-step explanation:

1) Previous concepts

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".

2) Solution to the problem

On this case we want to test is $\mu_{2}>\mu_{1}$ but we can rewrite this expression like this:

And if we reorder this las expression we got this:

$\mu_{2}- \mu_{1}>0$

So the correct system of hypothesis for this case would be:

Null hypothesis: $\mu_{2} - \mu_{1}\leq 0$

Alternative hypothesis: $\mu_{2} - \mu_{1} > 0$

On the other way would be:

Null hypothesis: $\mu_{2} \leq \mu_{1}$

Alternative hypothesis: $\mu_{2} > \mu_{1}$