Chapter PII, Problem 22RE

(a)

To determine

To create a scatterplot and describe the trend you see.

Explanation of Solution

It is given in the question that the organization Kids Count monitors issues related to children and the table is also given which shows a $50$ -state average of the percent of expectant mothers who smoked cigarettes during their pregnancies. Thus, the scatterplot of the data is constructed as follows:

  

Thus, we can say by looking at the scatterplot that the points in the scatterplot is moving downward from left to right and the points are in a straight line, so the association between them is negative and linear in nature and also as time goes on the percentage of expectant mothers smoking decreases.

(b)

To determine

To find the correlation.

Answer to Problem 22RE

The correlation is $0.972$ .

Explanation of Solution

It is given in the question that the organization Kids Count monitors issues related to children and the table is also given which shows a $50$ -state average of the percent of expectant mothers who smoked cigarettes during their pregnancies.So, we will find out the correlation for this by using the excel function for the two arrays by the function:

  $=\text{CORREL}(\text{array1, array2})$

Thus, the calculation for the correlation is as follows:

Correlation=

=CORREL(C31:C44,D31:D44)

Thus, the result for the correlation will be as:

Correlation=

-0.972

(c)

To determine

To explain how is the value of the correlation affected by the fact that the data are averages rather than percentages for each of the $50$ states.

Answer to Problem 22RE

It will be strengthened.

Explanation of Solution

It is given in the question that the organization Kids Count monitors issues related to children and the table is also given which shows a $50$ -state average of the percent of expectant mothers who smoked cigarettes during their pregnancies. Thus, the value of the correlation will be strengthened by the fact that the data are averages rather than percentages for each of the $50$ states because all the outliers in the data are averaged out.

(d)

To determine

To write a linear model and interpret the slope in context.

Answer to Problem 22RE

The linear model is $\text{<mo> \%^</mo> smoking while pregnant}=946.17-0.4662\times \text{Year}$ .

Explanation of Solution

It is given in the question that the organization Kids Count monitors issues related to children and the table is also given which shows a $50$ -state average of the percent of expectant mothers who smoked cigarettes during their pregnancies.Thus, for constructing a linear model we will use Excel as we will first select the data in Excel and then go to the insert tab from where we will select the scatterplot option in the charts and when the scatterplot is constructed we will go to the design tab under the chart tools, from where we will select the quick layout option and select the layout with the equation option then the linear model is constructed in the scatterplot as:

  

Thus, the linear model is:

  $\begin{array}{l}\widehat{y}=a+bx\\ \Rightarrow \text{<mo> \%^</mo> smoking while pregnant}=946.17-0.4662\times \text{Year}\end{array}$

Thus, the slope of the regression line is interpreted as that every year the percentage of smoking expectant mothers decreases by $0.4662$ percent.