Chapter 3.1, Problem 19E

(a)

To determine

Interpretation of correlation for the relationship between the calories and sodium in 17 brands of meat hot dogs.

Answer to Problem 19E

There is fairly strong and positive association between the calories and sodium in 17 brands of meat hot dogs.

Explanation of Solution

Given information:

Correlation,

  $r=0.87$

  

When r is positive, positive linear correlation exists.

When r is negative, negative linear correlation exists.

For weak correlation,

  $0<\left|r\right|<0.5$

For moderate correlation,

  $0.5<\left|r\right|<0.8$

For strong correlation,

  $0.8<\left|r\right|<1$

Note that

The association between the calories and sodium in 17 brands of meat hot dogs is strong and positive association.

(b)

To determine

Effect of hot dog brand with the smallest calorie content on the correlation.

Answer to Problem 19E

The linear correlation coefficientr would increase.

Explanation of Solution

Given information:

Correlation,

  $r=0.87$

  

Note that

In the scatterplot, the point corresponding with the lowest calorie content does not lie in the general linear pattern of the rest of the data points.

Thus,

The removal of this point from the data set makes the data appear more linear.

Hence,

There will be increase in linear correlation coefficient.