The mean annual beer consumption per person is 22 gallons A

The mean annual beer consumption per person is 22 gallons. A random sample of 300 residents yielded a mean annual beer consumption of 27.8 gallons. Assume the standard deviation is 55 gallons.

a. create a 95% confidence interval

Solution

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 =    27.8          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    55          
n = sample size =    300          
              
Thus,              
              
Lower bound =    21.57627846          
Upper bound =    34.02372154          
              
Thus, the confidence interval is              
              
(   21.57627846   ,   34.02372154   ) [ANSWER]