Chapter 8, Problem 29E

(a)

To determine

To find out what is the correlation between tar and nicotine.

Answer to Problem 29E

  $r=0.961$ .

Explanation of Solution

In the previous question, it is given the researcher wants to find out is the nicotine content of a cigarette related to the “tars”. Thus, a collection of data in milligrams on $29$ cigarettes produced the scatterplot, residual plot and the regression analysis shown in the question. And also it is given that,

  $R^2=92.4\%$

Thus, the value of correlation between tar and nicotine is as:

  $\begin{array}{l}{r}^2=R^2\\ \Rightarrow r^2=0.924\\ \Rightarrow r=\sqrt{0.924}\\ \Rightarrow r=0.961\end{array}$

(b)

To determine

To explain what would you predict about the average nicotine content of cigarettes that are two standard deviations below average in tar content.

Explanation of Solution

In the previous question, it is given the researcher wants to find out is the nicotine content of a cigarette related to the “tars”. Thus, a collection of data in milligrams on $29$ cigarettes produced the scatterplot, residual plot and the regression analysis shown in the question. Thus, we would predict about the average nicotine content of cigarettes that are two standard deviations below average in tar content that nicotine should be $1.922$ standard deviations below average. That is as,

  $\begin{array}{l}r=\frac{z_y}{z_x}\\ \Rightarrow -0.961=\frac{z_y}{2}\\ \Rightarrow z_y=-1.922\end{array}$

(c)

To determine

To find out what do you suspect is true about its tar content.

Explanation of Solution

In the previous question, it is given the researcher wants to find out is the nicotine content of a cigarette related to the “tars”. Thus, a collection of data in milligrams on $29$ cigarettes produced the scatterplot, residual plot and the regression analysis shown in the question. As it is given if a cigarette is one standard deviation above average in nicotine content, then it is true that tar should be $0.961$ standard deviations above average. As,

  $\begin{array}{l}r=\frac{z_y}{z_x}\\ \Rightarrow 0.961=\frac{z_y}{1}\\ \Rightarrow z_y=0.961\end{array}$