Question: The problem I struggled with this week is 8.1.27. It seemed like all the rest of the problems in the first chapter, but I got it wrong because I used “0” instead of the µ1-µ2 value. Not sure when I am supposed to use that value or how it is determined. I used the “view an example” feature to figure out I was supposed to put it in there for the homework, but I am worried about the quiz and not being able to recognize the situation it is needed.

Answer: When we are comparing two samples, whether means or proportions pay close attention to the claim. Here, the claim is that the difference in the two mean salaries is more than $5000. That requires the claim to be the alternative hypothesis since “more than” is a > operator, which is an inequality. So, Ha: μ₁ – μ₂ > $5000.

I know. You are saying that you don’t see a claim. But when a problem asks a question as this one does, that is the claim to be tested unless you find a more definitive claim later in the problem.

Note that you need to follow the “standard” format which is that we consider μ₁– μ₂ and not the reverse because that is the way the claim is stated in the problem: Region 1 is mentioned before Region 2. I think it might be less confusing if the problem had compared Alabama and Florida salaries, but the first entity (population) mentioned is logically μ₁.

Here is the StatCrunch solution:Pick-a-Problem: What difference does it make? 8.1.27