Consumption of alcoholic beverages by young women of drinking age in the United

Question

Consumption of alcoholic beverages by young women of drinking age in the United Kingdom, the United States, and Europe was reported(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. Click on the website logo to reference the data. 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).

Explanation / Answer

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    130          
t(alpha/2) = critical t for the confidence interval =    2.093024054          
s = sample standard deviation =    65.3911309          
n = sample size =    20          
df = n - 1 =    19          
Thus,              
              
Lower bound =    99.39600869          
Upper bound =    160.6039913          
              
Thus, the confidence interval is              
              
(   99.39600869   ,   160.6039913   ) [ANSWER]

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If you use z distribution for this, then this would be the solution. However, most likely the above one is what you use, because you only have 20 samples. Anyway, this is an alternative:

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    130          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    65.3911309          
n = sample size =    20          
              
Thus,              
              
Lower bound =    101.3415999          
Upper bound =    158.6584001          
              
Thus, the confidence interval is              
              
(   101.3415999   ,   158.6584001   ) [ANSWER]

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