You have been doing research for your statistics class on the prevalence of severe binge drinking among teens. You have decided to use 2011 Monitoring the Future (MTF) data that has a scale (going from 0 to 14) measuring the number of times teens drank 10 or more alcoholic beverages in a single sitting in the past 2 weeks.
a. According to 2011 MTF data, the average severe binge drinking score, for this sample of 914 teens, is 1.27, with a standard deviation of 0.80. Construct the 95% confidence interval for the true average severe binge drinking score.
b. One of your classmates, who claims to be good at statistics, complains about your confidence interval calculation. She or he asserts that the severe binge drinking scores are not normally distributed, which in turn makes the confidence interval calculation meaningless. Assume that she or he is correct about the distribution of severe binge drinking scores. Does that imply that the calculation of a confidence interval is not appropriate? Why or why not?