Chapter 3.2, Problem 23AYU

To determine

Draw a scatter diagram treating age of the mother as the independent variable.

Answer to Problem 23AYU

  

Explanation of Solution

Given information:

A biologist would like to know how age of mother affects the incidence rate of Down syndrome the data to the right represent the age of the mother and the incidence rate of Down syndrome per $1000$ pregnancies.

Draw a scatter diagram treating age of the mother as the independent variable would it make sense to find the of best fit for these data? Why or why not?

  $\begin{array}{cccccccccccccc}\begin{array}{l}Ageof\\ mother,x\end{array}& 33& 34& 35& 36& 37& 38& 39& 40& 41& 42& 43& 44& 45\\ IncidenceofDownSyndrome,y& 2.4& 3.1& 4& 5& 6.7& 8.3& 10& 13.3& 16.7& 22.2& 28.6& 33.3& 50\end{array}$

Calculation:

Consider the table,

  $\begin{array}{cccccccccccccc}\begin{array}{l}Ageof\\ mother,x\end{array}& 33& 34& 35& 36& 37& 38& 39& 40& 41& 42& 43& 44& 45\\ IncidenceofDownSyndrome,y& 2.4& 3.1& 4& 5& 6.7& 8.3& 10& 13.3& 16.7& 22.2& 28.6& 33.3& 50\end{array}$

The scatter diagram is,

  

There is line to fit the data a linear pattern. It is for sure a curve that is increasing with the values of $x$ that is the age of mother.

As the age of mother increases the chances of Down syndrome drastically increases.

Hence,the Down syndrome drastically increases with age of the mother increases.