Questions: Country, Chocolate Eaten, Nobel Prizes Won Australia, 4.5, 5.5 Austria, 8.5, 24.4 Belgium, 4.4, 8.6 Brazil, 2.9, 0 Canada, 3.9, 6 China, 0.7, 0 Denmark, 8.5, 25.3 Finland, 7.3, 7.6 France, 6.3, 9 Germany, 11.6, 12.7 Greece, 2.5, 1.9 Ireland, 8.8, 12.8 Italy, 3.7, 3.2 Japan, 1.8, 1.4 Netherlands, 4.5, 11.5 Norway, 9.4, 23.4 Poland, 3.5, 3.1 Portugal, 1.9, 2.2 Spain, 3.6, 1.7 Sweden, 6.4, 31.9 Switzerland, 11.9, 32.8 United Kingdom, 9.7, 18.8 United States, 5.3, 10.6 Find the value of the correlation coefficient

Country, Chocolate Eaten, Nobel Prizes Won Australia, 4.5, 5.5 Austria, 8.5, 24.4 Belgium, 4.4, 8.6 Brazil, 2.9, 0 Canada, 3.9, 6 China, 0.7, 0 Denmark, 8.5, 25.3 Finland, 7.3, 7.6 France, 6.3, 9 Germany, 11.6, 12.7 Greece, 2.5, 1.9 Ireland, 8.8, 12.8 Italy, 3.7, 3.2 Japan, 1.8, 1.4 Netherlands, 4.5, 11.5 Norway, 9.4, 23.4 Poland, 3.5, 3.1 Portugal, 1.9, 2.2 Spain, 3.6, 1.7 Sweden, 6.4, 31.9 Switzerland, 11.9, 32.8 United Kingdom, 9.7, 18.8 United States, 5.3, 10.6 Find the value of the correlation coefficient
Transcript text: \begin{tabular}{lrr} Country & Chocolate Eaten & Nobel Prizes Won \\ Australia & 4.5 & 5.5 \\ Austria & 8.5 & 24.4 \\ Belgium & 4.4 & 8.6 \\ Brazil & 2.9 & 0 \\ Canada & 3.9 & 6 \\ China & 0.7 & 0 \\ Denmark & 8.5 & 25.3 \\ Finland & 7.3 & 7.6 \\ France & 6.3 & 9 \\ Germany & 11.6 & 12.7 \\ Greece & 2.5 & 1.9 \\ Ireland & 8.8 & 12.8 \\ Italy & 3.7 & 3.2 \\ Japan & 1.8 & 1.4 \\ Netherlands & 4.5 & 11.5 \\ Norway & 9.4 & 23.4 \\ Poland & 3.5 & 3.1 \\ Portugal & 1.9 & 2.2 \\ Spain & 3.6 & 1.7 \\ Sweden & 6.4 & 31.9 \\ Switzerland & 11.9 & 32.8 \\ United Kingdom & 9.7 & 18.8 \\ United States & 5.3 & 10.6 \\ & & \end{tabular} Find the value of the correlation coefficient
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Solution

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Solution Steps

Step 1: Calculate Covariance

The covariance between the two variables \( X \) (Chocolate Eaten) and \( Y \) (Nobel Prizes Won) is calculated as follows:

\[ \text{Cov}(X,Y) = 25.9073 \]

Step 2: Calculate Standard Deviations

Next, we calculate the standard deviations of both variables:

\[ \sigma_X = 3.2021 \]

\[ \sigma_Y = 10.22 \]

Step 3: Calculate Correlation Coefficient

The correlation coefficient \( r \) is computed using the formula:

\[ r = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y} \]

Substituting the values we have:

\[ r = \frac{25.9073}{3.2021 \times 10.22} = 0.7916 \]

Final Answer

The correlation coefficient is given by:

\[ \boxed{r = 0.7916} \]

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