Question 10.29

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. Use Table G to test the null hypothesis that the population correlation against the alternative . Are the results significant at the 5% level?
  2. 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. 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.

10.29

(a) , the correlation is significantly greater than 0 at the 5% level. (b) States with more adult binge drinking are more likely to have underage drinking. . 10.24% of the variation in underage drinking can be accounted for by the prevalence of adult binge drinking. (c) Even though most states were used, it is assumed that sampling took place for each state; thus, we can still infer about the true unknown correlation (had we obtained different samples from each state, we would have gotten different results).