Question

Do graduates from UF tend to have a higher income than students at FSU, five years after graduation? A random sample of 100 graduates was taken from both schools. Let muf be the population mean salary at UF and let mufsu be the population mean salary at FSU. How should we write the alternative hypothesis?
A. Ha: mufsu - muf = 0
B. Ha: mufsu - muf > 0
C. Ha: mufsu - muf < 0
D. Ha: mufsu - muf does not equal 0

Answer 1

Answer:

C. Ha: mufsu - muf < 0

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 $\mu_{UF}>\mu_{FSU}$ but we can rewrite this expression like this:

$\mu_{FSU}$ since are equivalent expressions. And if we reorder this las expression we got this:

$\mu_{FSU}- \mu_{UF}$

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

Null hypothesis: $\mu_{FSU} - \mu_{UF}\geq 0$

Alternative hypothesis: $\mu_{FSU} - \mu_{UF} < 0$