Randomization
For Exercises 33–36, repeat the indicated ...

Question

Randomization

For Exercises 33–36, repeat the indicated exercise using the resampling method of randomization.

Powerball Jackpots and Tickets Sold Exercise 14

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says a biologist collects the data on the average rainfall in centimeters and the number of plant species observed in 10 different regions. She then adds an 11th region with unusually high rainfall and a low number of species. Using the randomization method, is there enough evidence to support a linear correlation between rainfall and species count? How does the inclusion of the 11th region affect the statistical results compared to the 1st 10 regions? So there are actually two parts to this problem, so we're gonna focus on the first part. Using the randomization method, is there enough evidence to support a linear correlation between rainfall and species count? And here we're just going to first begin by looking at the information that we're given on the problem. And the only piece of information that we're given in the problem is our sample size. Since we're looking at 10 different regions, that means our sample size N is going to be equal to 10. And this is the only piece of information that we're actually given. Now, in order to use the randomization method, we would actually need data on the number of plant species, as well as the average rainfall for these 10 regions. And since we don't have that, that information, there is insufficient information to actually use the randomization method. So, our answer for the first part of this problem is going to be that the information provided in the problem is insufficient to apply the randomization method, so we cannot determine whether the evidence supports a linear correlation. So now let's focus on the second part of this problem, which is how does the inclusion of the 11th region affect the statistical results compared to the 1st 10 regions. And if we look at the information that we're given about the 11th region, we're told that it has unusually high rainfall, as well as a low number of species. So that means that this data point is going to be an outlier. And since this data point has a high amount of rainfall and a low number of species, It will likely make the correlation coefficient more negative, indicating a stronger negative linear relationship. The P value associated with this would also likely decrease, because outliers increase the extremity of the observed correlation, which would lower our P value. So the answer to the second part of this problem is going to be that the inclusion of the 11th region strengthens the evidence uh for a linear correlation, likely in the negative direction between rainfall and species count. And the added region actually decreases the correlation coefficient, since it's making it more negative, and lowers the P value. So, that's going to be the answer to the second part of this problem. So, just to recap, The answer for the first part of the problem is the information provided in the problem is insufficient to apply the randomization method, though we cannot determine whether the evidence supports a linear correlation, and the answer to the second part of our problem is that the inclusion of the 11th region strengthens the evidence for a linear correlation, likely negative, between rainfall and species count, and the added region decreases the correlation coefficient and lowers the P value. So those are going to be the answers for this problem. So, I hope that this explanation has been useful, and I'll see you in the next video.

Randomization
For Exercises 33–36, repeat the indicated exercise using the resampling method of randomization.
Powerball Jackpots and Tickets Sold Exercise 14

Key Concepts

Randomization

Resampling Method

Powerball Jackpots and Tickets Sold

Watch next

RandomizationFor Exercises 33–36, repeat the indicated exercise using the resampling method of randomization.Powerball Jackpots and Tickets Sold Exercise 14

Key Concepts

Randomization

Resampling Method

Powerball Jackpots and Tickets Sold

Watch next

Randomization
For Exercises 33–36, repeat the indicated exercise using the resampling method of randomization.
Powerball Jackpots and Tickets Sold Exercise 14