Question 6 (5 points):

The table below lists the caloric contents and the fat contents (in grams) of 6-to 8-ounce servings for 10 hot chocolate products.

| Calories | 262 | 140 | 150 | 159 | 120 | 140 | 185 | 150 | 80 | 80 |
|----------|-----|-----|-----|-----|-----|-----|-----|-----|----|----|
| Fat (g) | 6.3 | 2.0 | 3.5 | 3.5 | 2.5 | 3.5 | 6.8 | 3.0 | 3.0 | 2.5 |

Find the correlation coefficient $ r $.

A. 0.59
B. 0.77 grams
C. 0.77
D. 0
E. -0.77

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Question 7 (5 points):

Continuation of Question 6. Based on the correlation value obtained in Question 6, what can you say about the relationship between calorie content and fat content of 6-to 8-ounce servings of hot chocolate products?

A. Moderate, positive, linear association
B. Strong, negative, linear association
C. Strong, positive, linear association
D. Weak, positive, linear association

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Question 8 (5 points):

Continuation of Question 7. Let's interchange the x and y variables, and recalculate the correlation coefficient. What is the new correlation value?

A. 0
B. -0.77
C. 0.77 grams
D. 0.59
E. 0.77

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. In this case, the variables are the calorie content and fat content of different hot chocolate products. A correlation coefficient close to 1 indicates a strong positive linear association, meaning that as one variable increases, the other tends to increase as well. The correlation coefficient of 0.77 suggests a strong positive linear relationship between the calorie content and fat content of these products.

This implies that when the calorie content of a hot chocolate product is higher, the fat content tends to be higher as well, and vice versa. In other words, products with more calories are likely to have more fat grams. This relationship can be attributed to the fact that fat is a dense source of calories, and products with higher fat content would naturally have higher calorie counts.

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