Identifying and interpreting a linear correlation P-value using its definition

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to identify and interpret a linear correlation P-value using its definition.  Here's our problem statement: For a data set of weights in pounds and highway fuel consumption amounts in miles per gallon of 10 types of automobile, the linear correlation coefficient is found, and the P-value is 0.004.  Write a statement that interprets the P-value and includes a conclusion about linear correlation.

Solution

OK, here, uh, the statement they want us to write is already mostly written.  We just have to fill in a few of the blanks.  The first part of the statement says, "The P-value indicates that the probability of a linear correlation coefficient that is at least extreme as something percent."  Well, this first part is the definition of the P-value itself.  And so when they give you the P-value and they're asking you for, again, the P-value, but here notice the percent sign.  They want you to take this decimal and convert it to a percent.

That's easy enough done.  Just move that decimal place over two places to the right.  So 0.004 becomes 0.4; this is a very low value.  And of course when the P-value is low, that indicates that there's statistical evidence for a linear correlation.  And that's really all there is to it.  Fantastic!

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