Exercise 821 Algorithmic Consumption of alcoholic beverages

Exercise 8.21 (Algorithmic)}

Consumption of alcoholic beverages by young women of drinking age has been increasing in the United Kingdom, the United States, and Europe (The Wall Street Journal, February 15, 2006). Data (annual consumption in liters) consistent with the findings reported in The Wall Street Journal article are shown for a sample of 20 European young women.

Excel or Minitab users: The data set is available in file named Alcohol. All data sets can be found on the premium online website.

Assuming the population is roughly symmetric, construct a 95% confidence interval for the mean annual consumption of alcoholic beverages by European young women (to 1 decimal).
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Solution

The degree of freedom =n-1=20-1=19

Given a=1-0.95=0.05, t(0.025, df=19) =2.09 (from student t table)

So the lower bound is

xbar - t*s/vn=133 - 2.09*72.2/sqrt(20) =99.3

So the upper bound is

xbar + t*s/vn =133 + 2.09*72.2/sqrt(20)=166.7