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Chapter 3: Q.21 (page 161)

Hot dogs Are hot dogs that are high in calories also high in salt? The figure below is a scatterplot of the calories and salt content (measured as milligrams of sodium) in 17brands of meat hot dogs.

(a) The correlation for these data is r=0.87. Explain what this value means.

(b) What effect would removing the hot dog brand with the lowest calorie content have on the correlation? Justify your answer.

Short Answer

Expert verified

a). In a hot dog, there is a very significant positive relationship between calories and salt.

b). The linear association would become more significant.

Step by step solution

01

Part(a) Step 1: Given Information

The calories and salt content (measured as milligrams of sodium) in 17brands of meat hot dogs.

02

Part(a) Step 2: Explanation 

The stronger the positive connection, the closer the correlation, r, is to 1.

In a hot dog, there is a very significant positive relationship between calories and salt.

03

Part(b) Step 1: Given Information

The calories and salt content (measured as milligrams of sodium) in 17brands of meat hot dogs.

04

Part(b) Step 2: Explanation 

The point in the bottom left corner (corresponding to the lowest calorie content) does not follow the same general linear trend as the other data points in the scatterplot.

Thus, deleting this point from the data set would make the data look more linear, resulting in a rise in the linear correlation coefficient r. (close to 1).

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