Chapter PII, Problem 7RE

(a)

To determine

To find out what is the correlation between pH and BCI.

Answer to Problem 7RE

  $r=-0.52$ .

Explanation of Solution

It is given in the question that biologists studying the effects of acid rain on wildlife collected data from streams in the Adirondack mountains. The scatterplot of BCI against pH is also given. And we have,

  $\begin{array}{l}{R}^2=27\%\\ n=163\end{array}$

The correlation between pH and BCI is calculated as,

  $\begin{array}{l}{r}^2=R^2\\ \Rightarrow r^2=-0.27\\ \Rightarrow r=-\sqrt{0.27}\\ \Rightarrow r=-0.52\end{array}$

(b)

To determine

To describe the association between these two variables.

Explanation of Solution

It is given in the question that biologists studying the effects of acid rain on wildlife collected data from streams in the Adirondack mountains. The scatterplot of BCI against pH is also given. And we have,

  $\begin{array}{l}{R}^2=27\%\\ n=163\end{array}$

  $r=-0.52$

Thus, by looking at the correlation and the scatterplot of BCI against pH we can say that the association between these two variables is negative and somewhat linear and not very strong because pH increases, variations in BCI also increases.

(c)

To determine

To explain what would you predict about the BCI if a stream has average pH.

Answer to Problem 7RE

It will have average BCI.

Explanation of Solution

It is given in the question that biologists studying the effects of acid rain on wildlife collected data from streams in the Adirondack mountains. The scatterplot of BCI against pH is also given. And we have,

  $\begin{array}{l}{R}^2=27\%\\ n=163\end{array}$

  $r=-0.52$

Thus, as we know by the scatterplot as pH increases then the variations in the BCI also increases, so we can say that if a stream has average pH, then we predict that it will also has average pH.

(d)

To determine

To explain what would you predict about the BCI in a stream where the pH is three standard deviations above average.

Answer to Problem 7RE

It will be $1.56$ standard deviations of BCI below the mean BCI.

Explanation of Solution

It is given in the question that biologists studying the effects of acid rain on wildlife collected data from streams in the Adirondack mountains. The scatterplot of BCI against pH is also given. And we have,

  $\begin{array}{l}{R}^2=27\%\\ n=163\end{array}$

  $r=-0.52$

Thus, in a stream where the pH is three standard deviations above average, we assume that the slope is half and then we will multiply it by three standard deviation then it will be $1.56$ standard deviations of BCI below the mean BCI.