Question

You suspect that freshmen from Utah cook dinner for themselves a different number of times than freshmen from Colorado. Perform a hypothesis test to determine if your suspicion is correct. The null hypothesis is LaTeX: H_0: ~ \mu_1=\mu_2H 0 : μ 1 = μ 2. Use a level of significance of LaTeX: \alpha = 0.05α = 0.05. What is the appropriate alternative hypothesis?

Answer 1

Answer:

Null hypothesis: $\mu_{U} - \mu_{C}= 0$

Alternative hypothesis: $\mu_{U} - \mu_{C} \neq 0$

Or equivalently:

Null hypothesis: $\mu_{U} = \mu_{C}$

Alternative hypothesis: $\mu_{U} = \mu_{C}$

Step-by-step explanation:

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".

Solution to the problem

Let $\mu_U$ the mean observed for Utah and $\mu_C$ the mean observed for Colorado.

On this case we want to test is $\mu_{U}=\mu_{C}$ but we can rewrite this expression like this:

And  on this case the last statement needs to be on the alternative hypothesis, and the complement in the null hypothesis

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

Null hypothesis: $\mu_{U} - \mu_{C}= 0$

Alternative hypothesis: $\mu_{U} - \mu_{C} \neq 0$

Or equivalently:

Null hypothesis: $\mu_{U} = \mu_{C}$

Alternative hypothesis: $\mu_{U} = \mu_{C}$