10.29 Correlation between the prevalences of adult binge drinking and underage drinking. A group of researchers compiled data on the prevalence of adult binge drinking and the prevalence of underage drinking in 42 states.12 A correlation of 0.32 was reported.

  1. (a) Test the null hypothesis that the population correlation ρ = 0 against the alternative ρ > 0. Are the results significant at the 5% level?

  2. (b) Explain this correlation in terms of the direction of the association and the percent of variability in the prevalence of underage drinking that is explained by the prevalence of adult binge drinking.

  3. (c) The researchers collected information from 42 of 50 states, so almost all the data available was used in the analysis. Provide an argument for the use of statistical inference in this setting.