Identifying and interpreting critical R values

Intro

Howdy!  I am Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to identify and interpret critical R values.  Here's our problem statement: For a data set of chest sizes (distance around chests in inches) and weights (pounds) of 12 anesthetized bears that were measured, the linear correlation coefficient is R = 0.873.  Use the table available below to find the critical values of R based on a comparison of the linear correlation coefficient R and the critical values.  What do you conclude about a linear correlation?

Part 1: Identify the critical R values

OK, so here we have an icon where we can access the table of critical values for R.  So we click that.  Here's our table of critical R values.  We need to find the number of pairs of data that we have, and you're given that in the problem statement right up here where it says “12 anesthetized bears,” so 12 is the number that we want to look for.  Here's the number 12 in the table of critical R values.  Corresponding with 12 is 0.576.

Now keep in mind that you have two critical values: one positive and one negative.  Only the positive one is listed here in the table.  So we go to put our answer in.  I'm going to start by putting in this plus-or-minus sign.  You could actually list the answers separately; I think it would take it that way as well — this one negative and then comma and then the other one positive.  But I like to make it easy and not type so much.  So I'm just going to put in a plus or minus sign and then the value from the actual R table.  Well done!

Part 2: Interpret the critical R values

Now, the next part of the problem: “Since the correlation coefficient R is” and then there's a drop down menu — “in the left tail below the negative critical value,” “in the right tail above the positive critical value,” “between the critical values.”  So in order to understand where we're at, it's helpful to draw a number line with your critical values and the value of R generated by your data.  To help us with that, I've actually produced something of a number line here in Excel.

So here we can put in our critical R values.  So we have one that's negative and one that's positive.  Now the question is “Where does our R value lie?”  0.873 lies in this region here, which is a region of acceptance.  So here in this first drop down menu in our answer fields, we're going to select “in the right tail above the positive critical value.”  And we're in a region of acceptance, so there is sufficient evidence to support the claim of a linear correlation.  Excellent!

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