Chapter 8, Problem 24E

(a)

To determine

To explain why each statement is incorrect.

Explanation of Solution

It is given in the question that a sociology student investigated the association between a country’s literacy rate and life expectancy then they drew the conclusions. The conclusion was “The literacy rate determines $64\%$ of the life expectancy for a country”. This is incorrect because the $R^2$ measures the amount of variation that is accounted for. It does not mean that x will determine the values of y . in this case, literacy rate accounts for $64\%$ of the observed variation in life expectancy.

(b)

To determine

To explain why each statement is incorrect.

Explanation of Solution

It is given in the question that a sociology student investigated the association between a country’s literacy rate and life expectancy then they drew the conclusions. The conclusion was “The slope of the line shows that an increase of $5\%$ in literacy rate will produce a two-year improvement in life expectancy. This conclusion is incorrect because this interpretation implies that there is a casual relationship. Even though two variables may be related, this does not mean that one causes the other. In this case, one could say that a $5\%$ increase in literacy rate is associated with an average two-year improvement in life expectancy.