In Exercises 25–28, refer to the data in the table below. The ...

Question

In Exercises 25–28, refer to the data in the table below. The entries are for five different years, and they consist of weights (metric tons) of lemons imported from Mexico and U.S. car crash fatality rates per 100,000 population [based on data from “The Trouble with QSAR (or How I Learned to Stop Worrying and Embrace Fallacy)” by Stephen Johnson, Journal of Chemical Information and Modeling, Vol. 48, No. 1].
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Conclusion If we were to use the sample data and conclude that there is a correlation or association between lemon imports and crash fatality rates, does it follow that lemon imports are the cause of fatal crashes?

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Conclusion If we were to use the sample data and conclude that there is a correlation or association between lemon imports and crash fatality rates, does it follow that lemon imports are the cause of fatal crashes?

Accepted Answer

Hi, everyone, let's take a look at this practice problem. This problem says the table below shows data collected over 5 years, including the number of ice cream cones sold in thousands, and the number of drowning incidents reported at public beaches during the same years. If we were to use the sample data and conclude that there is a correlation or association between ice creams cells and drowning incidents, does it follow that ice cream cells are the cause of drowning incidents? We're also given a table that has three columns. In the first column, we have the year, and it has values of 2019, 2020, 2021, and 2022, and 2023. In the second column, we have ice cream sales in thousands, and it has the values of 45, 50, 55, 60, and 65. And in the third column, we have drowning incidents, which has the values of 30, 35, 40, 42, and 47. We're also given four possible choices as our answers. For choice A, we have ice cream sales directly cause more drowning incidents. For choice B, there is a correlation, but no direct causal relationship between ice cream sales and drowning incidents. For choice C, since the two variables are statistically linked, we can conclude that drowning incidents are increasing due to increase in ice cream sales. And for choice D, people who eat more ice cream are more likely to drown. So, we're told in this problem that if we were to use the sample data, that we could conclude that there is a correlation or association between ice cream sales and drowning incidents. So what we need to do here is sort of differentiate between correlation and causation. So recall that correlation means that two variables tend to change together. So in this case, an increase in ice cream sales coincides with the increase of drowning incidents. However, causation means that one variable directly causes the other. So just because the two variables are correlated, does not mean that one causes the other. So, in our data here, we may have a positive correlation between ice cream sales and drowning incidents. It does not mean that eating ice cream causes drowning. Instead, there may be another factor, such as hot weather, that likely influences both variables. So take hot weather, for example. When we have hot weather, that increases the demand for ice cream, and it also leads to people swimming more, which could increase the likelihood of a drowning incident to occur. And so the above, so the observed correlation is likely due to this common external factor of hot weather, rather than a direct cause and effect relationship. So that means that while we may see an association or correlation between our two variables, there is no causal relationship. Therefore, we see that the correct conclusion corresponds to answer choice B. There is a correlation, but no direct causal relationship between ice cream sales and drowning incidents. So I hope that this explanation has been useful, and I'll see you in the next video.

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Key Concepts

Correlation vs. Causation

Confounding Variables

Statistical Significance

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