Interpreting r
In Exercises 5–8, use a significance leve...

Question

Interpreting r

In Exercises 5–8, use a significance level of α = 0.05 and refer to the accompanying displays.

Bear Length and Weight The lengths (inches) and weights (pounds) of 54 bears are obtained from Data Set 18 “Bear Measurements” in Appendix B, and results are shown in the accompanying XLSTAT display. Is there sufficient evidence to support the claim that there is a linear correlation between length and weight?

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So, first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. The heights in units of feet and trunk diameters in units of inches of 50 oak trees were obtained, and the correlation of the results that are obtained are shown in the accompanying XLSTAT output. And then we have our table for the XLSTAT output with our far right column being the diameter, our middle column being the height, and our far right, far left column being the variable. So once again, Our our far right column is diameter and our far left is our variable column. And for our variables, we have for the height, and then we have for the diameter. So for the height, we have 1, and then for the diameter, we have 0.843. And for the diameter for the height, we have 0.843, and then for the diameter diameter, we have 1. The P value for the correlation between height and diameter is 0.00001. At a significance level of alpha is equal to 0.05, is there sufficient evidence to support the claim that there is a linear correlation between tree height and trunk diameter? Awesome. So it appears for this particular prom we're ultimately trying to figure out whether or not there is sufficient evidence to support the claim that there is a linear correlation between tree height and trunk diameter, and that is what we're ultimately trying to solve for. So now that we know what we're trying to solve for, our first step that we need to take in order to solve this particular problem is we need to know to once again that we are trying to test whether there is a significant linear correlation between tree height and trunk diameter. And with that in mind, we now need to determine our null hypothesis and our alternative hypothesis. So let us call our null hypothesis H0, and for our null hypothesis, we can say that P is equal to 0, meaning that there is no linear correlation, and then for our alternative hypothesis, we'll call this H1, we can say that P cannot equal 0, meaning linear correlation does exist. Awesome. So with that in mind, our second step now is we need to focus our attention on using the XLSTAT output. So, let's take a moment here to pause and In case that's a term you're not familiar with, this XLSTAT is a statistical and data analysis software add-in tool for Microsoft Excel. So when we use this add-in tool in our Microsoft Excel spreadsheet, we can determine that from our XLSTAT output, we can say that the correlation coefficient, which we'll call R, is equal to 0.843. And this indicates strong positive linear relationship, and that will also mean that our P value, which I'll call PV for short, that PV or P value is equal to 0.0000, so 4001. Awesome, so 0.00001. Awesome. So now, our third step is we need to recall and use the decision rule. So we need to compare the P value to the significance level. Let's recall that our significance level alpha is equal to 0.05. So, if the P value, as we should recall, if our P value is less than or equal to alpha, then we will reject the null hypothesis. So I'll put an X and then put H0 next to it. So an X means we're going to be rejecting the null hypothesis. Fantastic. And if, for this case, so now we know the if condition, so we need to note that 0.0000. 0, wait. So, let's see, make sure we get our all of our zeros here. We have 1234, so we have 40s. 1, so we can state that 0.00001 is definitely less than 0.05. So that means because this is the case, we can reject the null hypothesis. Awesome. So that means our fourth and final step. we can make our final conclusions. So with everything we discovered together, we can state that there is sufficient evidence at the 0.05 significance level to support the claim that there is significant linear correlation between tree height and trunk diameter. So that will mean, without a doubt that our final answer will have to be. There is strong evidence to support the claim that there is linear correlation between tree height and trunk diameter, and that's it. We've officially solved for this problem. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. I

Key Concepts

Correlation Coefficient (r)

Significance Level (α)

Hypothesis Testing

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