Exercise 4.26 discusses a sample of households in the US. We are interested in determining whether or not there is a linear relationship between household income and number of children.
(a) Define the relevant parameter(s) and state the null and alternative hypotheses.
(b) Which sample correlation shows more evidence of a relationship, r = 0.25 or r = 0.75?
(c) Which sample correlation shows more evidence of a relationship, r = 0.50 or r = −0.50?

Exercise 4.26

For a random sample of households in the US, we record annual household income, whether the location is east or west of the Mississippi River, and number of children. We are interested in determining whether there is a difference in average household income between those east of the Mississippi and those west of the Mississippi.