Question

Listed below are annual data for various years. The data are weights​ (metric tons) of imported lemons and car crash fatality rates per​ 100,000 population. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value using

alpha

equals0.05

Is there sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality​ rates? Do the results suggest that imported lemons cause car​ fatalities?

Lemon_Imports_(x)   Crash_Fatality_Rate_(y)
230   15.9
266   15.7
357   15.5
481   15.2
532   14.8

The linear correlation coefficient r is

​(Round to three decimal places as​ needed.)

Answer 1

The scatter plot of the data is as shown -

The correlation coefficient is calculated in following 3 steps -

So, the correlation coefficient is approximately r = -0.978.

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Now, the significance of the correlation can be tested in following steps -

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A significant correlation only tells us about the strength of linear relationship between two variables which in this case is strong because the magnitude of the correlation coefficient is close to 1. But correlation doesn't establish a cause-effect relationship. So, it would be totally wrong to conclude that the imported lemons cause car fatalities.

For example, there might be a significant correlation between 'your sleeping hours over a month' and 'number of deaths in your country in these 30 days'. But would it mean that your sleeping more or less causes the change in number of deaths per day? The answer would be absolutely NO.

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